signal processing manual 2009

8/8/2019 Signal Processing Manual 2009

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Electronic Laboratory Manual

EE-402 Signal Processing

Seventh Semester

Electronic Engineering Department

By

Irfan Ahmed Usmani (Assistant Professor)

Fawad Shaukat (Assistant Professor)M. Fahad Wallam (Student, 2006 Batch)

Electronic Engineering DepartmentSir Syed University of Engineering & Technology

University Road, Karachi 75300http://www.ssuet.edu.pk/
http://www.ssuet.edu.pk/http://www.ssuet.edu.pk/


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SIR SYED University of Engineering & Technology, KarachiElectronic Engineering Department

EE 402 Signal Processing

Contents

Lab Laboratory Exercises Page

Simulation based Labs

1 MATLAB Fundamentals 12 Continuous-Time Signals 43 Discrete-Time Signals 74 Sampling of Analog Signals 105 Convolution and Correlation 146 Discrete Fourier Transform 177 Filters 198 Introduction to Simulink 23

Hardware based Labs9 Introduction to DSP Kit and related

Softwares26

10 Building an Audio Effect Processor 3411 i) LED Dancing Program

ii) Reading the Switch Value3839

12 i) Sound Playing Demoii) Digital Amplifier

4243

13 i) Echo Generation

ii) Reverb Generation

45

4714 i) Digital Sound Recorder

ii) PWM Generation4951


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Signal Processing Lab 1

1 MATLAB fundamentals:

In this course we will use software MATLAB to implement and simulate digital signal processingalgorithms.The name MATLAB stands for MATrix LABoratory. Originally MATLAB was developed to dealwith only one single but universal data type: the matrix.

A matrix is defined by [1] Its associated name

The number of rows

The number of column

The value of all matrix elements

The matrix data type includes vectors, for the case when either of the number of rows or thenumber of column equals to 1; and it includes scalars when both the number of rows andcolumns equal 1. Furthermore, matrices can be either real-valued or complex valued, which is themost general case.There is a small tutorial in this exercise for newcomer to become familiar with the MATLABfundamentals. It is recommended to try out introduced methods while solving the described tasks.

1.1 How to get help?There are several methods in MATLAB to access texts, which explain the usage and behavior of given

functions:

The HELP command is the basic help feature to get help of a function. For example, to get helpon the SUM function, type at the command prompt:

help sum

HELPWIN is used in the same manner as help, but it opens a separate window with advancesearch facilities and links to related topics.

HELPDESK uses a window of an installed web browser to display the help texts.

If the name of a command is not exactly known, the LOOKFOR function helps by seekingthrough the first comment line of all available functions and listing all functions where a desired

expression is found.

1.2 Statement, expressions and variables:MATLAB is an expression language. The expressions you type are interpreted and evaluated. MATLAB

statements are usually of the form

variable = expression, or simply

expression

Expressions are usually composed from operators, functions and variable names. Evaluation of the

expression produces a matrix, which is then displayed on the screen and assigned to the variable for future

use.

A statement is normally terminated with the carriage return. However, a statement can be continued to the

next line with three or more periods followed by a carriage return. On the other hand, several statements

can be placed on a single line if separated by commas or semicolon.

1.2.1 The variable ANS:

If the variable name and = sign are omitted, a variable ANS (for answer) is automatically created to whichthe result is assigned.

1.2.2 Suppressing screen output:If the last character of a statement is a semicolon, the printing is suppressed, but the assignment is carried

out. This is essential in suppressing unwanted printing of intermediate results.

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1.2.3 Colon notation:Colon notation is used to generate vectors, and reference submatrices, known as subscripting. Creative use

of this feature makes MATLAB programming code simple, readable and minimizes the use of loop, which

slows MATLAB.

An index vector is created by using the colon notationfirst : last

For example, [ creates the vector]5:1 [ ]54321 . An spacing can be introduced between two elements of a vector by using the colon notation

first : spacing : last

For example, [ creates the vector]5:2:1 [ ]531 .

1.3 Workspace:The contents of all the variables are stored in the MATLAB workspace. This is the memory region

allocated for variable.

The command WHO lists all variable which currently exist in the workspace.

WHOS additionally lists the size and amount of allocated memory.

The entire workspace or single variable can be cleared by using the CLEAR command.

1.4 Elementary operations:Algebraic expressions can be formed by the following basic operations:

Transpose of a vector/matrix can be produced by.

e.g..B

+ is used to add two vectors/matrices of identical size, or a vector/matrix and a scalar, e.g.

[ ] [ ]69;4754;23 + - subtracts two vectors/matrices of identical size, or a vector/matrix

B2 performs element-wise multiplication of two vectors/matrices of identical size, or a

vector/matrix and a scalar. For example, to square all elements of

B , we may write

BB performs element-wise division of two vectors/matrices of identical size, or a vector/matrix

and a scalar. For example, the reciprocal of all elements in

/B is computed through

B/1 performs vector/matrix multiplication. The number of columns in the first vector/matrix must

equal to the number of rows in the second. Example:

1.5 and complex matrices:

general, any matrix within the MATLAB can be complex-valued. However, for efficient storage,

gned, by default, the value

BB

Real

In

MATLAB distinguishes between real-valued and complex-valued matrices. Real valued matrices are

matrices where the imaginary parts of all matrix elements are zero. The following essentials must be knownto deal with complex-valued matrices:

The variables i and j are assi 1=i . This is used to define thecomplex values. For example,

10*5 j+

generates a complex-valued variable.

matrix can be extracted by using the function REAL and

o produce the complex conjugate of a matrix.

The real part of a complex-valuedimaginary part can be extracted by using the function IMAG. Both functions deliver the real-

valued matrices as outputs.

The function CONJ is used t

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The special character generates the complex conjugate transpose of a matrix, the hermitianmatrix. This character is written after an expression or variable.

For example, the hermitian of a matrix A can be obtained through:

'A

1.6 M-files:

MATLAB can execute a sequence of statements stored in a file. Such files are called M-files because theyhave .m extension as the last part of their file name.

There are two types of M-types:

Script files

Function files1.6.1 Script file:In a script file, script is a sequence of commands as they could be entered at the prompt. The script allows

to execute the entire sequence multiple times in a comfortable way, or to test modified versions.

1.6.2 Function file:In a function file, function has the additional feature of passing parameters. On calling a function, it may

read input arguments and after execution it may return output values. The FUNCTION command

specifies the input and output parameters of a function. It must be very first command in a function file.

Only comment may be written before the FUNCTION command. Any text after a % sign inside an m-file

is comment.

1.7 Flow control:In MATLAB flow control means that a program may not only be executed straight down from top to

bottom but with branches and repetitions.

The FOR function allows to create a loop which is controlled by a counter.

More general exit conditions can be implemented in a WHILE loop.

The IF command allows for conditional programming, together with ELSE.

All these commands come along with an END command which acts as a closing brace, togetherwith the opening brace, i.e. the introducing FOR, WHILE or IF command.

Exercise 1:Task # 1: Try all help methods to get help of any function.

Task # 2: (a) Assign 10 samples, from 0 to 9, of time to the vector t.

(b) Assign a vector of samples without assigning it to a variable.

(c) Assign 10 samples, from 0 to 9, of time to any vector without printing it to screen.

Task # 3: Investigate the difference between multiplication and element-wise multiplication of

vectors/matrices.

Task # 4: Generate a complex-valued matrix

( ) )10:1(*10,1 ionesa += and calculate the absolute square of all elements of all elements of this matrix.

Task # 5: Implement a function

[x]=sinewave(t)

which produces a sine wave of 1001 samples with spacing of mst 1= .Task # 6: Use MATLAB help to get familiar with the syntax ofFOR, WHILE and IF-ELSE statement.

Task # 7: Use FOR loop to generate a single vector y, which is a digitized unit sine wave with ten samples

per cycles, with 100 elements.

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1 Continuous Time Signals:

1.1 Generation and Plotting of Continuous Time Signals:A principle advantage of MATLAB in signal Processing is the simplicity with which signals of all types

can be generated and plotted. MATLAB supports a large variety of functions to visualize numerical data,

both as 2D and 3D graphs. The following basic features are often needed in our context of signal

processing:

The function PLOT is the basic method for plotting 2D graphs.

A single figure window can be split into several graphs with the SUBPLOT command.Some examples will serve here to show how simple commands can readily be used to produce useful

signals and plots.

1.1.1. Sine Wave Generation:The following commands will generate and plot 31 samples of a unit sine wave with a period of6.28 samples.

x=0:1.0:30;

y=sin(2*pi*x/(2*pi));

plot(y); grid on; title('Sine wave with period = 2pi');

xlabel('Sample number'); ylabel('Amplitude')

The first command establishes the vector =x [ ].30.....2,1,0 The next command generates the sine wavevector with the same number of elements as . Note that the first index of is 1, not 0, with period ofy x y

2 and a total of 31 samples, consists of 4.75 cycles of the sine wave.y

The Plotcommand, along with grid, title,xlabel andylabel, causes the plot shown in the above figure.

With simple commands like these, one can usually create process and plot signals rapidly and efficiently.

Here are few more examples to generate and plot different signals.

1.1.2. Cosine wave:

x=0:1.0:30; y=cos(2*pi*x/(2*pi));

plot(y); grid on; title('cosine wave with period = 2pi');

xlabel('Sample number'); ylabel('Amplitude')

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1.2. Simultaneous Plot:

MATLAB provides facility to plot more than one signal on the same axis. One can plot multiple signals by

using a single Plotcommand or by holding the first signal plot before plotting the second signal.Hold on

andHold offcommands is used to hold the plot. Different colors and different line types can be used to plotmultiple signals on the same axis.

>> x=0:0.1:20;

>> y=sin(x);>> z=cos(x);

>> plot(x,y,x,z)

Following sequence of commands also generate the same plot. This method holds first signal before

plotting the second signal.

>> plot(x,y)

>> hold on

>> plot(x,z,'g')>> hold off

1.3. Sub plotting:A single figure window can be split into several graphs with the SUBPLOT command. Here is an

example to get an idea about sub plotting.

>> t=linspace(0,20,300); %generates 300 equally spaced points between 0 and 20

>> x=sin(t);

>> y=cos(t);

>> z=tan(t);

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>> subplot(2,2,1);

>> plot(t,x)

>> title('sine wave')

>> xlabel('time')

>> ylabel('Amplitude')

>> subplot(2,2,2);

>> plot(t,y)>> title('cosine wave')

>> xlabel('time')

>> ylabel('Amplitude')

>> subplot(2,2,3);

>> plot(t,z)

>> title('tan wave')

>> xlabel('time')>> ylabel('Amplitude')

Exercise 1:

Task#1: Investigate all the arguments (line type and line color) ofPlotcommand by using MATLAB help.

Try to change the color and line type of the plot in the above examples.Task#2: Investigatesubplot command by using MATLAB help to understand the above example.

Task#3: Generate a decaying sinusoid with 1001 samples and spacing mst 1= . Plot the result withreference to tome. Try to change the color and line type of the plot. Switch on the grid. Use xlabel,

ylabel and title commands to name the X-axis, Y-axis and the plot.Task#4: Make a function to solve task#3 and call it from the workspace to get the plot.Task#5: Write a functiony=u(t) to plot the unit step function, defined as zero for input argument value less

than zero and one for input argument values greater than and equal to zero.

Task#6: Write a functiony=rect(t) to plot the rectangular function, Uses the definition of rectangle

function in terms of unit step function.Task#7: Write a functiony=tri(t) to plot a triangular function, defined as 1-|t| for |t| 1 and zero otherwise.

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1 Discrete-Time (DT) Signals:

A discrete-time signal x(n) is a function of an independent variable n, which is an integer. Adiscrete-time signal is not defined at instants between two successive samples.

1.1. Discrete-Time Signal Functions:

Sinusoids are as important in DT signal and systems analysis as in CT signal and systemanalysis. Sinusoids can be defined in a manner analogous to their CT counterparts as

+=

N

nAng

2cos][

or ( )+= nAng cos][ or ( ) += fnAng 2cos][

where:

A =real constant

=real phase shift, rad

=Fundamental period, samples per cyclesN

and f and are related to through = =N N/1 f 2/ .There are some important differences between CT and DT sinusoids. The first is the fact that ifwe create a DT sinusoid by sampling a CT sinusoid, their period may not be the same and, infact, the DT sinusoid may not even be period periodic. Let a DT sinusoid

[ ] ( )+= KnAng 2cos

1.2. Discrete-Time Signal Representation:

The following methods are use to illustrate the discrete-time signals:

1.2.1. Sequence representation:

( ) KK ,1,3,3,1,2,1,3 =

nx

Where arrow ( ) represents the reference time 0=t

1.2.2. Functional representation:

( )

== =

=

=

=

33

1221

13

3,01

n

nn

n

n

nx

1.2.3. Tabular representation:

n 3210123

( )nx 1331213

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1.2.4. Simultaneous Plot:

1.3. Sub plotting:

Exercise 1:

Task#1: Investigate all the arguments (line type and line color) ofPlotcommand by using MATLAB help.Try to change the color and line type of the plot in the above examples.

Task#2: Investigatesubplot command by using MATLAB help to understand the above example.

Task#3: Generate a decaying sinusoid with 1001 samples and spacing mst 1= . Plot the result withreference to tome. Try to change the color and line type of the plot. Switch on the grid. Use xlabel,

ylabel and title commands to name the X-axis, Y-axis and the plot.Task#4: Make a function to solve task#3 and call it from the workspace to get the plot.Task#5: Write a functiony=u(t) to plot the unit step function, defined as zero for input argument value less

than zero and one for input argument values greater than and equal to zero.

Task#6: Write a functiony=rect(t) to plot the rectangular function, Uses the definition of rectangle

function in terms of unit step function.Task#7: Write a functiony=tri(t) to plot a triangular function, defined as 1-|t| for |t| 1 and zero otherwise.

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4. Sampling of Analog Signals:

Most signals of practical interest, such as speech, biological signals, seismic signals, radarsignals, sonar signals, and various communications signals such as audio and video signals, areanalog. To process analog signals by digital means, it is first necessary to convert them intodigital form, that is, to convert them to a sequence of numbers having finite precision. This

procedure is called analog-to-digital (A/D) conversion, and the corresponding devices are calledA/D converters (ADCs)

Conceptually, we view A/D conversion as a three step process. This process is illustrated infigure 4.1

1. SamplingThis is the conversion of a continuous time signal to a discrete time signal obtained by taking

samples of continuous time signal at discrete time instants. Thus, if xa(t) is the input to the

sampler, the output is xa(nT) x(n), where T is called the sampling interval.

2. QuantizationThis is the conversion of discrete time continuous valued signal into a discrete time, discrete

valued (digital) signal. The value of each signal sample is represented by a value selectedfrom a finite set of possible values. The difference between the unquantized sample x(n) and

the quantized output xq(n) is called the quantized error.

3. Coding

In the coding process, each discrete value xq(n) is represented by a b-bit binary sequence.

Sampler Quantizer

Coder

xq(x(n)

Digit

al

signal

Analo

g

signal

xa(t

Quantized

signal

Discrete

time signal

01010...

Figure 4.1: Basic parts of an analog-to-digital (A/D) converter.

There are many ways to sample an analog signal. We limit our discussion to periodic or uniformsampling, which is the type of sampling used most often in practice. This is described by therelation

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Where x(n) is the discrete time signal obtained by taking samples of the analog signal ( )txa every T seconds. This procedure is illustrated in figure 4.2. The time interval T betweensuccessive samples is called the sampling period or sample interval and its reciprocal 1/T=Fs iscalled the sampling rate (samples per second) or the sampling frequency (hertz).

1 2 3 4 5 6 7 8 9

T 2T 5T9T t=nT

xa(t)x(n)= xa(nT)

xa(t)

n0

x(n)

Figure 4.2: Periodic sampling of an analog signal

Periodic sampling establishes a relationship between the time variables t and n of continuoustime and discrete time signals, respectively. Indeed, these variables are linearly related throughthe sampling period T or, equivalently, through the sampling rate Fs= 1/T, as

sF

nnTt ==

There exists a relationship between the variable F (or) for analog signals and the frequencyvariable (or) for discrete time signals. To establish this relationship, consider an analog

sinusoidal signal of the form

( ) )2cos( += FtAtx a Which, when sampled periodically at a rate =1/T samples per second, yieldssF

( ) )2cos()( += FnTAnxnTxa

)2

cos(

+=

sF

nFA

The frequency variables F and are linearly related as

sF

Ff = (4.1)

or, equivalently, as

T= (4.2)

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The relation in (4.1) justifies the name relative or normalized frequency, which is sometimes used

to describe the frequency variable . As (4.1) implies, we can use to determine the

frequency F in hertz only if the sampling frequency is known.

f f

sF

The range of the frequency variable F or for continuous time sinusoids are


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Exercise:

Task#1: Write a script to generate a continuous time sinusoid signal with amplitude=2 for a time0 to 1 sec and taken the frequency as a user input by using input command.

Task#2: Write a script to convert continuous time signal of task#1 to a discrete time signal and

take the sampling frequency as input which should be less than twice the maximumsignal frequency in Hertz.Task#3: Write a script to convert continuous time signal of task#1 to a discrete time signal and

take the sampling frequency as input which should be equal to twice the maximum signalfrequency in Hertz.

Task#4: Write a script to convert continuous time signal of task#1 to a discrete time signal andtake the sampling frequency as input which should be greater than twice the maximumsignal frequency in Hertz.

Task#5: Write a script using subplot command to generate task #1, task#2, task#3 and task#4plots. Analyze the four plots, what happen by increasing the sampling frequency?

Task#6: Consider the analog signal

( ) )100cos(3 ttx a = (i) Determine the minimum sampling rate required to avoid aliasing.

(ii) Suppose that the signal is sampled at the rate Fs=200 Hz. What is the discrete timesignal obtained after sampling? Plot the discrete-time signal.

(iii) Suppose that the signal is sampled at the rate Fs=75 Hz. What is the discrete time signalobtained after sampling? Plot the discrete-time signal.

(iv) What is the frequency 0


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5. Convolution and Correlation:

5.1 Introduction:

Convolution and Correlation are closely related operations that are basic to many areas of digital signal

processing.

Convolution can be described as the integral of the product of two data sequences, with one of the sequences

reversed and shifted relative to the other.

Correlation function of the two sequences is the same as the convolution without the reversal of one of the

sequences. It may therefore be described as the integral of the product of two sequences with one shifted

relative the other. The correlation function is used as a measure of how well two sequences are correlated, or

agree with one another, or are like one another.

5.2 Mathematical Form:We assume that the two time series to be either convolved or correlated each have Msamples and can be

designated as follows:

[xk]=[x0

[yk]=[y0

x1 x2LxM1]

y1 y3LyM1]

This notation implies that both sequences have the same length, which may not be the case and indeed israrely with FIR filtering, where the data sequence is usually much longer than the impulse response. Whenthe sequences are of different lengths, we use the convention of adding zeros to the right end of the shortersequence. For example, if an FIR filter with impulse response [hk] and length 4 were processing an inputsignal [xk]of lengthM= 9, we would have

[xk]=[x0

[yk]=[h0

x1 x2

h1 h2

x3 x4 x5 x6 x7

h3 0 0 0 0 0]

x8]

The convolution function of the two sequences [xk]and [yk]is obtained by

cxy (n)=conv{[xk], [yk]}

n

=xkynkk=0

The function is referred to as the convolution sum of the inputs by the impulse response function and the

output is said to be given by the convolution of the input by the impulse response of the system.

This function may be extended to waveforms of infinite duration by writing them as

cxy (n)=

xkynkk=

=xk h k

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the generalized form of the convolution sum. In this equation is known as convolution star, signifies theoperation of convolution.

If the input consists of a continuous sequence of impulses then the above summation may be replaced by

integral.

cxy (t)=+

xytd=

This expression is known as convolution integral.

The Correlation function of the two sequences [xk]and [yk]is obtained by

rxy (n)=xcorr{[xk], [yk]}

n

=xnyn+kk=0

This function may be extended to waveforms of infinite duration by writing them as

rxy (n)=

xkyn+kk=

When [xk]and [yk]are different sequences, rxy (n)is the cross-correlation function. When [xk]and [yk]are same sequences, rxx (n)is the auto-correlation function.

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Exercise:

Task#1: Two data sequences are given as follows:

1321

=kx

1121 =

ky

Compute by hand the convolution function ( )nCxy .Task#2: Use conv command to compute the convolution function for the given data sequence in Task#1.

Task#3: In MATLAB, conv command (function) neither provides nor accepts any timing information if the

sequences have arbitrary support. To solve this inconvenience, write a function

[y, ny] = conv_m(x, nx, h, nh)

a simple extension of MATLAB function conv, which performs the convolution of the given

sequences with their timing information.

Task#3:Repeat Task#2 using conv_m function.

Task#4: Compute the convolution func ion Ct xy(n) of the following sequences:

010020100 =

kx

00006.08.0100

=ky

Task#5: Compute by hand the complete autocorrelation function of

{ }00010211 =kx

Task#6: Use xcorr command to compute the autocorrelation function of the sequence given in Task#5.

Task#7: Calculate the energy of the given sequence in Task#5. Compare the result with its autocorrelation

function at n=0.

Task#8: Compute the cross correlation function rxy(n) of the given sequences in Task 4, for n = 0 through 4.

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1. Discrete Fourier Transform:

The discrete Fourier transform (DFT) is one of the specific forms of Fourier analysis. It

transforms one function into another, which is called the frequency domain representation,

or simply the DFT, of the original function (which is often a function in the time domain).But the DFT requires an input function that is discrete and whose non-zero values have alimited (finite) duration. Such inputs are often created by sampling a continuous function,

like a person's voice. And unlike the discrete-time Fourier transform (DTFT), it only

evaluates enough frequency components to reconstruct the finite segment that was analyzed.

Its inverse transform cannot reproduce the entire time domain, unless the input happens to be periodic (forever). Therefore it is often said that the DFT is a transform for Fourieranalysis of finite-domain discrete-time functions. The sinusoidal basis functions of the

decomposition have the same properties.

Since the input function is a finite sequence of real or complex numbers, the DFT is idealfor processing information stored in computers. In particular, the DFT is widely employed

in signal processing and related fields to analyze the frequencies contained in a sampledsignal, to solve partial differential equations, and to perform other operations such as

convolutions. The DFT can be computed efficiently in practice using a fast Fouriertransform (FFT) algorithm.

The sequence of N complex numbers x0, ..., xN1 is transformed into the sequence of Ncomplex numbers X0, ..., XN1 by the DFT according to the formula:

where is a primitive N'th root of unity.

The transform is sometimes denoted by the symbol , as in or or .

2. Inverse Discrete Fourier Transform:

The inverse discrete Fourier transform (IDFT) is given by

A simple description of these equations is that the complex numbers Xk represent the

amplitude and phase of the different sinusoidal components of the input "signal" Xn. The

DFT computes the Xkfrom the Xn, while the IDFT shows how to compute the Xn as a sum

of sinusoidal components with frequency k / N cycles per sample.

In Matlab DFT can be find by using following commands:

FFT(X): is the discrete Fourier transform (DFT) of vector X. For matrices, the FFT operation isapplied to each column. For N-D arrays, the FFT operation operates on the first non-singleton dimension.

FFT(X,N): is the N-point FFT, padded with zeros if X has less than N points and truncated if it hasmore.

FFT(X,[],DIM) orFFT(X,N,DIM): applies the FFT operation across the dimension DIM.

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Exercise:

1001

=n

x

Task#1: Data sequence is given as follows:

Compute by hand the DFT function .k

X

Task#2: Use FFTcommand to compute the DFT function for the given data sequence in Task#1.

Task#3: Plot the magnitude and phase graphs of DFT function of Task#2 in separate window.

Task#4:Plot an

sequence. Where a=0.8 and define at n=0 to 35. Find its DFT, plot its magnitude and phase

graphs also.

Task#5: Taking the IDFT of the results of task #2 and verify that it gives you the same sequence as mention in

task#1.

Task#6: Design a DFT algorithm on C-language. The DFT is defined by the formula

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Filters:

Electronic filters are electronic circuits which perform signal processing functions, specifically to removeunwanted frequency components from the signal and/or to enhance wanted ones. Electronic filters can be:

passive or active analog or digital

high-pass, low-pass, band-pass, band-reject (band reject; notch), or all-pass.

discrete-time (sampled) or continuous-time

linear or non-linear

infinite impulse response (IIR type) or finite impulse response (FIR type)

The most common types of electronic filters are linear filters, regardless of other aspects of their design

Digital Filters:

A digital filter is a system that performs mathematical operations on a sampled, discrete-time signal to reduce

or enhance certain aspects of that signal. This is in contrast to the other major type of electronic filter, theanalog filter, which is an electronic circuit operating on continuous-time analog signals. An analog signal may

be processed by a digital filter by first being digitized and represented as a sequence of numbers, then

manipulated mathematically, and then reconstructed as a new analog signal. In an analog filter, the input

signal is "directly" manipulated by the circuit.

In digital signal processing applications, it is often necessary to change the relative amplitudes of frequency

components or remove undesired frequencies of a signal. This process is called filtering. Digital filters areused in a variety of applications. Digital filter design requires the use of both frequency domain and time

domain techniques. This is because filter design specifications are often given in the frequency domain, but

filters are usually implemented in the time domain with a difference equation. Typically, frequency domainanalysis is done using the Z-transform and the Discrete Time Fourier Transform (DTFT).

In general, a linear and time invariant digital filter with inputx(n) and outputy(n)may be specified by itsdifference equation.

(1)=

=

=M

k

k

N

i

i knyainxbny1

1

0

)()()(

where biand ak are coefficients which parameterise the filter. This filter is said to haveNzeros andMpoles.

Each new value of the output signal,y(n) , is determined by past values of the output, and by present and pastvalues of the input. The impulse response, h(n) , is the response of the filter to an input of (n) , and istherefore the solution to the recursive difference equation.

(2)=

=

=

M

k

k

N

i

i knhainbnh1

1

0

)()()(

There are two general classes of digital filters: infinite impulse response (IIR) and finite impulse response

(FIR). The FIR case occurs when ak= 0, for all k. Such a filter is said to have no poles, only zeros. In thiscase, the difference equation in (2) becomes

(3)

=

=1

0

)()(N

i

i inbnh

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Since (3) is no longer recursive, the impulse response is finite with lengthN.In the case where ak 0 , the difference equation usually represents an IIR filter. In this case, (2) will usuallygenerate an impulse response which has nonzero values as n. However, later we will see that for certainvalues of ak0 and bi, it is possible to generate an FIR filter response.

The Z-transform is the major tool used for analysing the frequency response of filters and their differenceequations. The Z-transform of a discrete time signal,x(n), is given by

(4)n

n

znxzX

=

= )()(

The DTFT may be thought of a special case of the Z-transform, wherez is evaluated on the unit circle in the

complex plane.

(5)jw

n

ez

jw

enx

zXeX jw

=

=

=

=

)(

|)()(

From the definition of the Z-transform, a change of variable shows that a delay ofKsamples in the time

domain is equivalent to multiplication by Z-kin the Z-transform domain.

[ ]

)(

)(

)(

)()(

)(

zXz

zmxz

zmx

zknxknx

k

m

mk

km

m

n

nz

=

+

=

=

=

=

=

(6)

We may use this fact to rewrite the equation (1) in the Z-transform domain, by taking Z-transforms of both

sides of the equation:

(8)=

=

=M

k

k

k

N

i

i

i zYzazXzbzY1

1

0

)()()(

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(9)

=

=

=+

1

01

)(]1)[(N

i

i

i

M

k

k

k zXzbzazY

=

=

+

==M

k

k

k

N

i

i

i

za

zb

zX

zYzH

1

1

0

1)(

)()( (10)

From this form, we see that any filter, which can be represented by a difference equation, has a rationaltransfer function (i.e. a transfer function which is a ratio of polynomials). From this result, we may compute

the frequency response of the filter by evaluatingH(z) on the unit circle.

=

=

+

=M

k

jwk

k

N

i

jw

ijw

ea

eb

eH

1

1

0

1

)( (11)

There are many different methods for implementing a general recursive difference equation. Depending on the

application, some methods may be more robust to quantisation error, require fewer multiplies or adds, or

require less memory. Fig. 1 shows a system diagram known as the direct form implementation; it works for

any discrete time filter described by a difference equation. Note that the boxes containing the symbolz1

represent unit delays, while a parameter written next to a signal path represents multiplication by thatparameter.

Figure 1: Direct form implementation for a discrete time filter described by a general difference equation21


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Exercise:

Task#1: Generate two sinusoid signals with frequency of 100 Hz and 400 Hz. Add these two signals. Designa filter to extract 100 Hz signal.

Task#2: Taking the signals of Task#1, design a filter to extract 400Hz signal.

Task#3: Generate the code for the given FIR filter, having the coefficient b0=1, b1= -1 and b2=1. Takingsinusoid as x(n) having 80 samples, frequency =1/8 and phase= pi/6.

y(n) = b0x(n) +b1x(n-1)+b2x(n-2)Task#4 Generate the code for the FIR filter in Task#3, having the coefficient b0=1, b1= -1 and b2=2. Taking

impulse signal as x(n) having 16 samples.

Task#5: Generate the code for the given IIR filter, having the coefficient b0=0, b1= 1 and a0=1, a1=0.97.Taking impulse signal as x(n) having 80 samples.

y(n) =x(n-1)+ay(n-1)

a=0.97

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1. Introduction to SIMULINKSimulink is a software package for modeling, simulating, and analyzing dynamical systems. Itsupports linear and nonlinear systems, modeled in continuous time, sampled time, or a hybrid ofthe two. Systems can also be multirate, i.e., have different parts that are sampled or updated atdifferent rates.

For modeling, Simulink provides a graphical user interface (GUI) for building models as blockdiagrams, using click-and-drag mouse operations. With this interface, you can draw the modelsjust as you would with pencil and paper (or as most textbooks depict them). This is a far cry fromprevious simulation packages that require you to formulate differential equations and differenceequations in a language or program. Simulink includes a comprehensive block library of sinks,sources, linear and nonlinear components, and connectors. To customize and create own blocksS-Functionscan be used, which is another skill.

MATLAB and Simulink are integrated; you can simulate, analyze, and revise your models ineither environment at any point.

1.1. Getting Started with Simulink

1.1.1. Opening Simulink Library Browser:

1. In the Matlab command window click on theSimulink Library Browser or just writeSimulink in Command window prompt.Expending these libraries can access variousToolboxes, Blocksets and Simulinkfunctions.

Fig. 1: Simulink Library Browser Fig. 2: Expended Libraries

2. Write Simulink3 in CW to get Simulink Block Library. This is another way of access SimulinkLibrary. Double clicking each icon will open the corresponding library.

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Blocksets and Toolboxes can be opened in the same way.

Fig. 3: Simulink Block Library

Fig. 4: Simulink Library of Blocksets and Toolboxes

1.1.2. Opening new Simulink model:

Click to create new model button on SLB.

Fig. 5: Opening New model(.mdl file)

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Exercise:

Task#1:(a): Using Simulink, plot a sine wave between t=0s and t=10s.(b): Using Simulink, plot a sine wave between t=0s and t=100s and also plot its Spectral

Density by setting Max step size to 0.02.

Task#2: Using Simulink, plot a Unit step Signal between t=0s and t=10s.

Task#3: Implement figure 6 in Simulink to understand the concept of synthesizing square wave.

Task#4: Implement the following continuous-time system with a Simulink model:y(t) = 0.2x(t) +0.8 x(t-2) -0.4x(t-5)

Simulate the system between t=0s and t=10s with the following inputs:a) x(t) = u(t) (Unit step)b) x(t) = 2.5 sin(2*pi*f*t)

Task#5: Make a Simulink Model to record and write wave file from a wave device for the

duration of 10 sec at 8khz sampling rate and it also show its time plot.

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1. Introduction to DSP Kit & related softwares:

1.1.Overview:The purpose of this lab is to familiarize you with DSP Kit TMS320C6711, Simulink,Real Time Workshop, Link for CCS and how they interact with Code Composer Studio

(CCS). This lab involves building relatively simple systems using Simulink rather thanCCS.

1.1.1. Hardware:

DSP Board: Texas Instruments TMS320C6711 (DSP Starter Kit) DSK DSP: Fixed-point and floating-point arithmetic, eight functional units (two

multipliers and six ALUs), 150 MHz clock (up to 900 MFLOPS), 32 general-

purpose registers of 32-bit word length, 64K (+2x4K) bytes internal memory,DMA controller (16 channels),external memory interface (32-bit address

space), multichannel serial port, host port interface.

External Memory: 16M bytes SDRAM at 100 MHz and 128K bytes flash-programmable ROM.

Figure 1: Hardware overview [2]

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Waveform Generator:Specifying Waveform Parameter Valuesa value for a

ctions:

Osc

e has rich triggering possibilities. Here we explain only the most

tures that might be necessary for accomplishing a particular task.

e

e

The

at allows you to get rid of random noise. The output

ainly caused

settings on a floppy disk. First, set up the oscilloscope's settings of your needs.

While working with the signal generator, you will often need to enter

parameter of the generated waveform. To do this, follow these instru

Turn the knob on the front panel of the signal generator until you reach thedesired value. You can also specify which digit to modify by pressing the > or< button. The flashing digit indicates the one that is incremented /decremented if you turn the knob.

illoscope:

Triggering

The oscilloscop

important fea

Setting up an external trigger. Press Edge in the trigger section of theoscilloscope's controls. Set triggering to external by pressing th

corresponding soft key Ext. Note, it is necessary to connect a BNC cable tothe Ext. Trigg. input on the scope's rear panel. We suggest to use external

triggering whenever it is possible.

Setting up triggering to a corresponding input channel. Press Edge in the

trigger section and choose either channel 1 or channel 2 by pressing the

corresponding soft key.

Us ful Features

re are also a number of very useful features that might help you.

feature th Averaging: asignal of the codec of our DSP board is relatively noisy. This is mby higher frequency noise and cable connection imperfections.

To enable averaging, push Acquire in the Waveform section of the

oscilloscope's front panel. On the display, choose Averaging by pressing thecorresponding soft key. Turn the knob to set up an appropriate number of

triggering events to be averaged (usually 4 or 8 will already give a sufficient

noise removal).

Auto scale: to quickly set up your oscilloscope, you can use auto scalingwhich tries to determine the parameters automatically. Press Auto Scale to

enable it.

Saving a screenshot: this feature allows you to save a screenshot of theoscilloscope's display to a floppy disk as an image file. So you can easilyinclude it in your report. To enable this feature, you first have to set some

parameters: press Utility > Print Config. Set Print to=Disk" and

Format=TIF". Now, to save the display to a floppy disk, just insert one in theinternal floppy drive and press Quick Print.

Saving oscilloscope's settings: this is a very useful feature that allows you tostore all current scope's settings in one of the three internal slots. You can

restore them whenever you need. You also have the possibility to save the

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When ready, push Save/Recall >Save and then choose a slot by pressing theTo soft key or press New File to store onto a floppy disk. Push Press to Save

to actually save the settings. To restore saved settings, press Save/Recall

!Recall , choose source by pressing From, and push Press to Recall to actuallyrestore the saved settings.

ware

de Composer Studio:

1.1.2. Soft

Co Before starting Code Composer Studio (CCS), ensure that the DSP board ised with power and connected to the PC.

There should be an icon on the desktop. If necessary, start CCS from the Starts >Texas Instruments >Code Composer Studio 2

CS to load a DSP program

after build". Press OK.

ery instruction to

one of the eight functional units and you should ensure that all eight units are

n Linear Assembly and C/C++, the

0 bits

its

typical DSP Program for Real-Time Block Processing usedt

main.c does the whole initialization and remains in an endless loop. The blocks.h provides constants for the block processing environment iggered

by the DMA's hardware interrupt. It manages circular buffers the DMA

alls the

provid

menu: Start >Program

('C6000)>Code Composer Studio.

For more convenience, you should enable C

automatically into the DSP's memory after a successful compilation/linking.

In CCS, choose Option>Customize. Press the Program Load Options tab andput a check mark on Load program

TMSC6000 Optimizing C Compiler

There are three possibilities to program TI's C6000 DSPs: Assembly, LinearAssembly, and C/C++. In Assembly, you have to allocate ev

working concurrently permanently. Ioptimizer takes this part. In this laboratory, we mostly use C/C++ and

sometimes hand-optimized assembly routines. C/C++ Data Types and Word

Lengths:

char 8 bits short 16 bits int 32 bits long 4 oat 32 bits double 64 bits pointer 32 bStructure of a

in his Laboratory

function init()is called, where you can do additional initializations.

isr_tttt.c contains the Interrupt Service Routine (ISR) which is tr

uses to transfer data between the memory and the codec and it c

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function processing() where the actual signal processing happens. The tttt

heapsize, ...)

lobal) objects (e.g. additional buffers or filter coefficients).

We or

rses/dsplab/.

In your home directory, you have to create the folder L:/DSP LAB/ where forhave to copy and unzip the required files. For

e source code files double-clicking opens the file in a text editor

window.

load it into the DSP's memory. It's also possible to do an

Incremental Build where only the modified files are compiled.

g loaded. It

might couse the DSP board or the the computer to halt.

For

suc

ope

does not run properly.

>Restart.

This problem happens very often, especially when it is the first program

is a substitution for the type of the actual working buffer (e.g. float or

short cmplx).

vectors.asm is the interrupt vector table. There must be an entry for the

ISR above.

lnk.cmd contains a memory map and arguments for the linker command(e.g. libraries,

userfiles The init() and processing() functions are defined here and all thenecessary (g

algorithm modules functions and structures for filters, _t, ...Building a Program in CCS

will provide you with most of the source code. You can find *.zip files f

the different experiments on our webpage psc.inw.tugraz.at/cou

each laboratory exercise you

some of the experiments, you have to modify or add source code. Allnecessary source files of a DSP program will be bundeled to a so-calledPROJECT.

In the main menu, choose Project>Open and select the *.pjt fileappropriate for your exercise. In the Project view window you can see alist of th

To build a project, choose Project>Rebuild All from the main menu. This

will (re)compile all the files of the project, link them to the resulting *.out

file, and

To run a program, choose Debug>Run or press the F5 button. Rememberthat the program must be successfully compiled, linked, and loaded into

the DSP's memory. Do not run the DSP without a program bein

more convenience, we sometimes provide a WORKSPACE file. Using

h a file opens the specified projects and editor windows automatically. To

n such a *.wks file, click File>Workspace>Open .

Troubles with CCS>Known Bugs

CCS built and loaded the interrupt-based program successfully but itRestart the DSP program: Debug

after starting CCS.

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Really nothing works any more.

problem happens when a big amount of data is

transmitted through the parallel connection (e.g. while debugging).

uLau

Tes on andinstallation. The following message is then displayed:

s that the first three switches, USER_SW1, USER_SW2, and,are all in the up (ON) position. Change the switches to (1 1 0 x)2

t two switches are up (press the third switch down). The fourthswitch is not used. Repeat the procedure to select GEL > Check DSK > Quick

UsiSimRea I C/C++ code

that can be compiled using CCS. The Embedded Target for TI C6000 DSP

programming interface) required by Real-Time

le.

isn

p

ith the C6711 DSK. These configuration setting are required andare similar for all the experiments. While this configuration generally has

red that these setting do exist. This is

Close (or kill) CCS, power-down and power-up the DSP board, and start

CCS again. This

Q ick Test of DSKnch CCS from the icon on the desktop. Press GEL >Check DSK > Quickt. The Quick Test can be used for confirmation of correct operati

Switches: 7Revision: 2

Target is OK

This assumeUSER_SW3

so that the firs

Test and verify that the value of the switches is now 3 (with the display

Switches: 3).You can set the value of the first three user switches from 0 to

7.Within your program you can then direct the execution of your code basedon these eight values. Note that the Quick Test cycles the LEDs three times.

A confidence test program example is included with the DSK to test and

verify proper operation of the major components of the DSK, such asinterrupts, LEDs, SDRAM, DMA, serial ports, and timers.

ng DSP Kit via Matlab:

ulink uses a block based approach to algorithm design and implementation.l-Time Workshop converts these Simulink models into ANS

provides the APIs (AdvancedWorkshop to generate code specifically for the C6000 platform. Link for CCS is

used to invoke the code building process from within CCS to build an executab

This code can then be downloaded on the target DSP from where it runs. Thapproach allows for rapid prototyping. Also, a model built once in Simulink ca

be made to run on various system as long as one has the appropriate Embedded

target toolbox.

Initial configuration (for all labs):This section describes how configure Simulink and Real-Time Worksho

for use w

to be done only once, it must be ensu

the first step in any experiment using Simulink.

Check if CCS is properly installed

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To verify that CCS is properly installed on the system, enter ccsboardinfoat the Matlab command line. Matlab should return information similar to

ollowing listing:

--------- --- --------------------------- --------------0 C6711 DSK 0 CPU_1 TMS320C6x1x

ter c6000lib es:

C6000: DSP Core Support, C62x DSP Library, C64x DSP Library, C6416

Support, C6711 DSK Board Support, RTDX Instrumentation,

Configuration Parameters for C6000 Hardware1. Launch Matlab

nch Simulink

the f

Board Board Proc Processor Processor

Num Name Num Name Type--- ------------------

To ensure Embedded Target for TI C6000 DSP is installed, en

Matlab should display the C6000 block library containing the librari

DSK Board Support, C6701 EVM Board Support, C6711 DSK Board

TMDX326040 Daughtercard Support.

Figure 2: Software overview

2. At the Matlab command line, type simulink to lau

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3. Create a new model in Simulink.

uration

Parametersime Workshop category.

e the Make command and Template makefile

7. Choose the Optimization category in the Select tree. For Simulation

8. Choose the TI C6000 target sel.... Set Code generation target type

9

10. In the Select tree, choose the Debug category. Select Verbose build

11. In the Select tree, choose the Solver category. Ensure that Solver is set

Building a Simple I/O system with the C6711 DSKTo build th

1. Perform the steps in section using DSP Kit via MATLAB.e Out, LineIn. The goal is to

e In jack and passesgnal through, unchanged, to the Headphone/Line out jack.

edded Target

4 to-Analog

Figure 3: Simple I/O

6. Double clicking a block displays the block parameters. Wh e parametersare userdefinable, others are not. The ADC source field ca t to either Mic

In or Line In. If the input one then the field should be set to

Mic In; otherwise, it should be set to Line In. In the ADC block, Stereo should

4. To open the Configuration Parameters, select Simulation!Config

5. In the Select tree, chose the Real-T

6. For Target Selection, choose the file ti c6000.tlc. Real-Time Workshopwill automatically chang

selections.

and Code generation, un-select Block reduction optimization andImplement logic signals....

to C6711DSK.. Choose the TI C6000 compiler. Set Symbolic debugging.

here.

to Fixed type / discrete.

e model for a Single Audio Effect, follow these steps:

2. The DSK has two input and output jacks: Lin

implement a system that accepts an audio signal via the Linthat si

3. Select the Simulink Library Browser window and select Emb

for TI C6000. Within this group, select the C6711 DSK Board Support library.There will be five (5) blocks displayed: ADC, DAC, LED, Reset, and Switch.

. Place the ADC (Analog-to-Digital Converter) and DAC (Digital-

Converter) blocks on your model by clicking and dragging.5. Once they are on your model, connect the two, as shown in figure 3.

Line In

ADC DAC

C6711 DSK C671

ADC

1 DSK

DAC

ile somn bese

is from the microph

be unchecked and the output data type set to integer. NOTE: The sample rate

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can also be set here. For most applications, this is either set to 8kHz (speechapplications) or 44.1kHz (music applications). The Samples per Frame

parameter tells the system how many samples to process at one time. The

greater the samples per frame, the longer it takes to process the signal (due tomemory needs and computational load).

. Double click the DAC block. Ensure that the Word Length field is thesame (16-bit) for both the ADC and DAC blocks.

. Save the model:

Select File > Save As > ...location

78

jack.ng the headphones to the Headphone jack.

1 eady to run. Verify that the DSK board

command on the Simulinkmodel toolbar (the icon with the 3 arrows) to begin compiling the model and

tran

uter,

12.

sembly code will be compiled and loaded

e CCS and return to the model in Simulink.

rite a brief report (2 to 3 pages) about your learning, observation and understanding of

is lab.

9. Ensure that the hardware is connected properly by:

(a) Connecting the microphone to the Mic In(b) Connecti

0. The model is now complete and r

is connected properly .Use the Incremental Build

sferring the code to the DSK.

11. If this is the first time the board has been used since turning on the compa DSK Startup window will open temporarily to configure the board.

The system will first compile code in Matlab, then Code Composer Studio

(CCS) will be opened, where as

onto the DSP. Once in CCS, a progress window will open as the code isloaded onto the board.

13. The program, once loaded will begin to run. Test the model by speaking

into the microphone and listening to your speech through the headphones.After verifying that the code works, stop the program by using the Halt

command in CCS. Clos

Task:

W

th

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1. Building an Audio Effect Processor:

1.1.Overview:In this laboratory exercise, students will create an audio effects processor usingTMS320C6711.The effects that have to be implemented are echo, reverberation and

flange.

1.1.1. Designing a single echo effect in real time

In the previous lab, a basic I/O system for audio was built, compiled and run. This section

investigates data manipulation and representation on the DSK by designing a single echo

filter.

In this section, an echo filter is designed. An echo is a delayed, attenuated version of the

original signal. The difference equation describing a system with a single echo is definedas

y[n] = x[n] + ax[n

D]

where a is the gain and D is the delay. Figure 1 shows the Simulink block diagram that

implements this filter.

1. Build and run the model in figure 1(using the Incremental Build button on the

model toolbar).

2. Add the C6711DSK target preferences block from the TI C6000 TargetPreferences block library. This block is not connected to any other block in the

model.3. Test the model using the microphone (Mic In) and a pair of headphones

(Headphone).

4. Change the delay and gain by double clicking on the desired block and explorethe effect of each on the output signal.

Figure 1:Real time single echo filter [1]

Z-40

C6711

DSK

Line In

C6711

DSK

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1.1.2. Real time audio reverberation model

In this section a model that simulates audio reverberation is created and built.

Reverberation is the result of an infinite number of echoes added together, and can be

represented mathematically as

y[n] = x[n]+ax[n

D]

bx[n

D]

Where a and b are the gains and D is the delay.

For this experiment, a microphone is connected to the Mic In connector on the C6711

DSK and speakers (and an oscilloscope) connected to the Line Out connector on theC6711 DSK. To test the model, speak into the microphone and listen to the output from

the speakers.

1. Open Simulink.

2. Create a new model by selecting File > New > Model from the Simulink

menu bar.3. Use Simulink blocks to create the model shown in figure 2.

4. The Integer Delay block is in Discrete library of the Simulink blockset. The

Gain block is in the Commonly Used library of the simulink blockset. The Line

In and Line Out block for the C6711 DSK are in the C6711 Board Supportlibrary of the Embedded Target for TIC6000 blockset.

5. From the TI C6000 Target Preferences block library, add the C6711DSK target

preferences block. This block is not connected to any other block in the model.6. Click the C6711 DSK ADC block to select it. Select Block Parameters from the

Simulink Edit menu. Set the following parameters for the block: Select the +20 dB mic gain boost check box

For Output data type, select Double from the list

Set Scaling to Normalize Set Source gain to 0.0

Enter 64 for Samples per frame

7. For ADC source, select Mic In.8. Click OK to close the Block Parameters: ADC dialog.

9. Now set the options for the C6711 DSK DAC block.

Set Scaling to Normalize

For DAC attenuation, enter 0.0 Set Overflow mode to Saturate.

10. Click OK to close the dialog.

11. Open the Configuration Parameters dialog, select Solver on the Select tree,and set the appropriate options on the Solver pane for your model and for the

target.

Under Solver options, select the fixed-step and discrete settings from the lists. Set the Fixed step size to auto and select Single Tasking for the Tasking mode.

12. Build and run the model (using the Incremental Build button on the model

toolbar).13. Speak into the microphone connected to the board. The model should generate

a reverberation effect out of the speakers, delaying and echoing the words you

speak into the mic.

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Figure 2: Real time reverberation filter [1]

Z-20

Reset

C6711 DSK

C6711 DSK

DACLine In

C6711 DSK

ADC

Audio Reverberation C6711 DSK Implementation

1.1.3. Real time audio flange model

A flange effect is a (time domain) audio effect, which is achieved by combining to

identical signal with each other, with one signal delayed by a gradually changing amount.

The difference equation for the flange effect is given by

y[n] = x[n] + ax[n

d(n)]

where the time varying delay is given by

d(n) = D + D2 (1 sin( 2_fdnfs))

where D is a fixed delay, fd is the flanging frequency, and fs is the sampling rate. Figure 3

shows the Simulink block diagram that implements this system.

1. Build and run the model in figure 3 (using the Incremental Build button on the

model toolbar).

2. Add the C6711DSK target preferences block from the TI C6000 TargetPreferences block library. This block is not connected to any other block in the

model.3. Test the system using recorded music or speech played through the Line In

connector of the DSK and a pair of headphones connected to the Headphone

connector.

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Reset

C6711 DSK

C6711 DSKLine In

C6711 DSK

ADC

Figure 3: Real time flange filter

Task:

Write a brief report (2 to 3 pages) about your learning, observations and understandings

of this lab.

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1. The LED Dancing Program:

1.1. Program Led.c:

#include "stdio.h"

#define LED_OFF 0x07000000#define msec 500void main(void)

{

int LED[]={0x06000000,0x05000000,0x03000000};short i=0,toggle=0;

comm_poll();

printf("The LED Dancing Program; Made By: M. Fahad Wallam");led_control(LED_OFF);

while(1)

{

led_control(LED[i]);delay_msec(msec);

if(i=2)

toggle=1;else

toggle=0;

if(toggle=0)i++;

else

i--;}

}

1.2. How it works:

This is a simple LED-dancing program that demonstrate you how to control LEDs on theDSK board. For controlling the LEDs the DSP processor must be in the 32-bit mode. You

also need to know the address of the IO port and the data bits to which the LEDs are

connected. But you do not have to worry

about all of it because I have written a function void led_control(value) where value is

the appropriate code for turning on/off the required LED. Below is the code for the

LEDs:

Codes Purpose

0x07000000 To turn off all 3 LEDs

0x06000000 To turn on the first LED

0x05000000 To turn on the second LED

0x03000000 To turn on the third LED

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Remember: The LEDs are connected in the common anode configuration.

Like wise, I have also written the function void delay(ms), where ms is the argument

that represents time in milliseconds, to make your life easier. In the above program, Ihave used the 500-millisecond time delay so that the turning on or off of an LED is

properly visible. Actually, the delay function uses the internal 32-bit timer (Timer 0) tocreate delay. The rest of the program is very simple to understand if you properly learnedthe C-programming language course in the second semester. To run this program

correctly you must include the following files:

1. C6xdsk.cmd

2. C6xdsk.h

3. C6xinterrupts.h

4. C6xdskinit.h

5. C6xdskinit.c

6. Vectors.asm (Note: you do not have to include Vectors_11.asm)

7. Ledcontrol.c8. Delay.c

9. Rts6701.lib

10. Led.c

All the files are provided by the Texas except ledcontrol.cand delay.c which is written

by myself. The description of all the files is given in the first chapter of the book

previously mentioned except ledcontrol.c and delay.c. The ledcontrol.c is used tocontrol the LEDs and the delay.c is used to produce time delay.

2. Reading the Switch Value:

2.1. Program Switch.c:

#include "stdio.h"

void main(void)

{

unsigned short sw,temp=37;

comm_poll();pritnf("The User Switches Reading Program; Made By: M. Fahad Wallam");

while(1)

{sw=sw_read();

if(sw!=temp)

{temp=sw;

printf("\nThe User Switch Value is %d",sw);

}}

}

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2.2. How it works:

It is also a very simple program that demonstrates how to read switch value from the

switches on the DSK board. For reading the Switches, again the DSP processor must bein the 32-bit mode. You also need to know the address of the IO port and the data bits to

which the switches are attached. You also have to shift the bits in order to get correctvalue. But do not get confused because I have also written a function shortsw_read(void) that reads the switch value from the user switches and return it as a short

type. Below is the table for the switch values:

SW3 SW2 SW1 Value

Off Off Off 000

Off Off On 001

Off On Off 010

Off On On 011

On Off Off 100On Off On 101

On On Off 110

On On On 111

To run this program correctly you must include the following files:

1. C6xdsk.cmd

2. C6xdsk.h

3. C6xinterrupts.h

4. C6xdskinit.h

5. C6xdskinit.c6. Vectors.asm (Note: you do not have to include Vectors_11.asm)

7. Switch_read.c

8. Rts6701.lib

9. Switch.c

All the files are provided by the Texas except switch_read.c and switch.c that is

written by myself.

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Tasks:

1. Write a program such that the first LED blinks three times, then second LED blinks

two times and then the third blinks only for one time. Reverse the order that is, thethird LED blinks for three times, then the second one blinks two times and the first

LED blinks one time. After that all three LED blinks three times. The processcontinues indefinitely.

2. Write a program such that when the user presses the switches the LEDs will be turnedon according to the following table:

SW3 SW2 SW1 LED3 LED2 LED1

Off Off Off Off Off Off

Off Off On Off Off On

Off On Off Off On Off

Off On On Off On On

On Off Off On Off OffOn Off On On Off On

On On Off On On Off

On On On On On On

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1. Sound Playing Demo:

1.1. Program Sound.c:

#include "stdio.h"

interrupt void c_int11(){

output_sample(input_sample());

}

void main(void)

{

comm_intr();printf("The Live Sound Playing Program; Made By: M. Fahad Wallam");

while(1)

{}

}

1.2. How it works:

It is a very simple program. It gives the output same as the input. This program uses the

onboard TLC320AD535 (AD535) codec. It supports the sampling rates up to 16KHz but,however, it is fixed at 8KHz on the board. It is interfaced with the serial port of the

processor. This program is an interrupt-based program. Every 125usec (1/8KHz) it givesan interrupt. Upon receiving an interrupt, the processor jumps to the interrupt vector table

from where it gets the address of that interrupt and jumps to that address that is, here, it

jumps to c_int11() function. Now, here, the function input_sample() reads the digitalvalue from the ADC and the function output_sample() write the digital value (which is

read by the input_sample() function) to the DAC.


1. C6xdsk.cmd

2. C6xdsk.h

3. C6xinterrupts.h

4. C6xdskinit.h

5. C6xdskinit.c

6. Vectors_11.asm

7. Sound.c

8. Rts6701.lib

All the files are provided by the Texas except sound.c that is written by myself.

You see how much it is simple!!!

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2. Digital Amplifier:

2.1. Program Digi_amp.c:

#include "stdio.h"

short unsigned gain;short output;

interrupt void c_int11()

{

output=gain*input_sample();output_sample(output);

}

void main(void)

{

comm_intr();printf("The Digital Amplifier; Made By: M. Fahad Wallam");

while(1)

{

}}

2.2 Program gain.gel:

menuitem "Gain Adjustment"slider Gain(0,40,1,1,gain_factor)

{

gain=gain_factor;}

2.3. How it works:

It is also a very simple experiment just to show you how a gel (general extension

language) is used to make a slider bar. GEL (General Extension Language) is an

interpretive language that allows you to write functions to configure the CCS IDE as wellas access the target processor or simulator. It allows you to automate tasks similar to

macros, however, its C-like syntax

allows it to be much more powerful!!! GEL supports basic C constructs such as while

loops and if structures. In the gain.gel program, the menuitem Gain Adjustmentcreates a sub menu on the gel menu bar with the name Gain Adjustment but when it

will be loaded (from fileLoad Gel). Also, slider Gain(1,40,1,1,gain_factor) creates an

item Gain with in the Gain Adjustment sub menu. Parameters required by the slider(from left to right) are: slider minimum value, slider maximum value, the change value

caused by an up or down click (or arrow keys) respectively and finally, the parameter to

which the slider value is assigned to.

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1. C6xdsk.cmd

2. C6xdsk.h

3. C6xinterrupts.h4. C6xdskinit.h

5. C6xdskinit.c

6. Vectors_11.asm

7. Digi_amp.c

8. Rts6701.lib

9. gain.gel

All the files are provided by the Texas except Digi_amp.c and gain.gel that is writtenby myself.

Task:

Write a program such that when the value on the slider bar is 1, 1Khz sine wave will be

produced, when the value on the slider bar is 2, 2Khz sine wave will be produced, when

the value on the slider bar is 3, 3Khz sine wave will be produced, when the value on theslider bar is 4, 4Khz sine wave will be produced, when the value on the slider bar is 0, no

output will be produced. For the generation of sine wave program see the example 1.1 in

the book previous mentioned.

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1. Echo Generation

1.1. Program Echo.c:

#include "stdio.h"

#define bufferlength 3000#define amplitude 5;short input;

int output;

int buffer[bufferlength];

short i = 0;


{input = input_sample();

output=input + 0.1*amplitude*buffer[i];

buffer[i] = input;output_sample(output);

i++;

if (i >= bufferlength)

i = 0;}

void main(void){

comm_intr();printf("The Echo Generation; Copied from the book written by Rulph Chassing");

while(1)

{}

}

1.2. How it works:

This experiment demonstrate you the power of DSP. The basic purpose of this program is

to introduce the sound processing techniques. The soul of the whole program is in theexpression given below:

Outputt = input + 0.1*amplitude*buffer[i];buffer[i] = input;

To explain these expression please analyze the following block diagram. Believe me, thisis the best way to understand. I have also visualized it with the help of the following

block diagram:

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The above figure is the block diagram of the Echo. In the above program, the delay factor

is calculated as:

Delay = 3000x125usec

Delay = 375 msec

Here, 125usec is the sampling time of the ADC and 3000 is the bufferlength of the

array, which is used as a delay-multiplying factor. You can see the effect by changing the

value of the bufferlength which is 3000 in above program. You can also change the

value of the amplitude which is 5 in the program.


1. C6xdsk.cmd

2. C6xdsk.h

3. C6xinterrupts.h4. C6xdskinit.h

5. C6xdskinit.c

6. Vectors_11.asm

7. Echo.c

8. Rts6701.lib

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2. Reverb Generation:

2.1. Program Reverbation.c:

#include "stdio.h"

#define bufferlength 3000#define amplitude 8;short input;

int output;

int buffer[bufferlength];

short i = 0;float old;

interrupt void c_int11(){

input = input_sample();

old=(float)buffer[i]*0.1*amplitude;output=(int)input+(int)old;

buffer[i]=output;

output_sample(output);

i++;if (i >= bufferlength)

i = 0;

}

void main(void){

comm_intr();

printf("The Reverb Generation; Made By: M. Fahad Wallam");while(1)

{

}}

2.2 How it works:

Reverberation is the result of the many reflections of a sound that occur in a room. This is

also a very simple program. If you have understood the last program, it is not difficult for

you to understand this program; otherwise, you will find yourself to thrash your headwith this program. Well, lets try to understand this program. Same as in the previous

program, the spirit of the whole program is in the expressions given below:

old=(float)buffer[i]*0.1*amplitude;

output=(int)input+(int)old;

buffer[i]=output;

To explain these expressions please try to analyze the following block diagram again.

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You have clearly noticed that the difference between the echo and reverberation is that

there is a positive feed back with the delay element in the reverberation while there isonly the delay element in the echo. The same analyzes is true for the case of

reverberation as that in the echo but remember the positive feed back path. Calculation of

delay element is also same as that in the case of echo.


1. C6xdsk.cmd

2. C6xdsk.h

3. C6xinterrupts.h

4. C6xdskinit.h

5. C6xdskinit.c

6. Vectors_11.asm

7. Reverberation.c

8. Rts6701.lib

All the files are provided by the Texas except Reverberation.c that is written by myself.

Task:

Write a program to produce the flange and chorus effect.

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1. Digital Sound Recorder:

1.1. Program digi_rec.c:

#include "stdio.h"

#define N 8000*8;unsigned short sw,i,j;far short buffer[N];


{if(sw==0)

output_sample(input_sample());

else if(sw==1 && ii)j=0;

if(sw==3 && j==0)

j=i+1;}

void main(void)

{short temp=37;

comm_intr();

printf("The Digital Recorder; Made By: M. Fahad Wallam");while(1)

{

sw=sw_read();if(sw!=temp)

{

temp=sw;if(sw==0)

printf("\nLive Play");

else if(sw==1)

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{i=0;

printf("\nRecording");

}else if(sw==2)

{j=0;printf("\nRecorded Sound Playing in the Forward direction");

}

else if(sw==3)

{printf("\nRecorded Sound Playing in the Reverse direction");

j=i+1;

}else

printf("\nInvalid switch!!!");

}}

}

1.2 How it works:

This is another very simple program. In this program, an array of size 8000x8 (equals to

16000) is declared which is used to store the samples of sound from ADC. The recordingwill be of 8 seconds long. As the sampling time of ADC is 8 KHz, this means that there

are 8000 samples in a second and I declare the size of an array is 8000x8=16000, so therecording time is 8 seconds. There are four options:

1) Just straight play (live play) that is no recording.2) Recording the sound.3) Play the recorded sound same as it was recoded.4) Play the recorded sound in the reverse direction.

The working of the first option is very simple and explained in the experiment 3(a). The

second one has just described in the above paragraphs. The third one is the same as the

first one except that the samples stored in the array are now sent to the DAC. In the lastone, the samples are sent from the end of the array instead of from the start of the array.

Surprised to look its simplicity!!! Yes, this is your simple digital sound recorder.


1. C6xdsk.cmd

2. C6xdsk.h

3. C6xinterrupts.h

4. C6xdskinit.h

5. C6xdskinit.c

6. Vectors_11.asm

7. Digi_rec.c

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8. Rts6701.lib

9. Switch_read.c

All the files are provided by the Texas except Digi_rec.c and Switch_read.c that arewritten by myself.

TASK [Optional]:

Write a program to modify this recorder as much as you can that is include the effects

like distortion, 3D effects, etc.

2. PWM (Pulse Width Modulation) Generation:

2.1. Program PWM.c:

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#include "stdio.h"

unsigned short amp_out,ton,toff;

float amp_in,count_on,count_off;

interrupt void c_int11(){if(ton==0 && toff==0)

{

ton=(short)count_on;

toff=(short)count_off;}

else

{if(ton>0)

{

output_sample(amp_out);led_control(0x0x00000000);

ton--;

}

else if(toff>0){

output_sample(0);

led_control(0x0x07000000);toff--;

}}

}

void main(void)

{

unsigned short temp1=37,sw,t1,t2,freq;float temp2,temp3,dc,f1,f2;

comm_intr();

printf("The Variable PWM with Variable Amplitude generation Program; Made By: M.

Fahad Wallam");while(1)

{

sw=sw_read();if(sw!=temp1)

{

printf("\nEnter the Frequency (1 to 4000Hz): ");scanf("%d",&freq);

printf("\nEnter the On Duty Cycle(%): ");

scanf("%f",&dc);printf("\nEnter the Amplitude (0 to 3V): ");

scanf("%f"&amp_in);

amp_out=(short)((amp_in/3)*32767);

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temp1=sw;dc=(dc/100);

f1=(dc/freq);

f2=((1-dc)/freq);count_on=8000/f1;

count_off=8000/f2;temp2=count_on;temp3=count_off;

while(temp2>=1)

temp2=temp2-1;

while(temp3>=1)temp3=temp3-1;

t1=temp2*1000;

t2=temp3*1000;

if(t1=t2 && t1!=0)

{count_on=count_on+1-temp2;

count_off=count_on-temp3;

}else

{if(t1!=0)

{

if(t1>=500)count_on=count_on+1-temp2;

else

count_on=count_on-temp2;}

else

count_on=count_on-temp2;

if(t2!=0){

if(t2>=500)

count_off=count_off+1-temp3;else

count_off=count_off-temp3;

}else

count_off=count_off-temp3;

}ton=0;

toff=0;

}

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}}

2.2 How it works:

You are already familiar with the concept of PWM that how it is generated from 555timer IC and from microcontroller, the terms regarding to PWM that is On-Duty Cycleand Off-Duty Cycle, etc. Lets try to explore this program. First of all we investigate how

variable PWM will be produced and then try to understand the variable amplitude

methodology. The formula for On-Duty Cycle is:

Duty Cycle% = [ton/(ton+toff)]x100

Duty Cycle% = (ton/T)x100

Where, T is the total time period. So,

T=1/F

Where, F is the frequency of the PWM.

Now, we are interested to find the ton and toff. But, first we have to divide the duty cycleby 100 because the user enters the value of duty cycle in percentage form. So, the

following expression performs this job for us:

dc=(dc/100);

Now, the next step is to find the value of ton, which can be found by simply transformingthe formula of On-duty cycle:

ton = (Duty Cycle/100)*Tton = (Duty Cycle/100)/F

But, we have already converted the percentage value in the decimal value so this isimplemented by the following expression:

f1=(dc/freq);

f1 is used in place of ton. Similarly, the toff can be found by the following expression:

f2=((1-dc)/freq);

f2 is used in place of toff. Now, we have to find the some integer value for the ton and

toff so that the processor can be able to know how long the signal must be in the on state

and how long it must be in the off state depending upon the frequency and the duty cycle.

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As we know that the sampling time of the codec is fixed at 8KHz, so the followingexpression fulfils our requirements:

count_on=8000/f1;count_off=8000/f2;

There is a problem with the above expressions that the value of the count_on andcount_off may have the decimal part. So, the following expressions are the solution of

this problem that is it discard the decimal part and approximate the their values:

temp2=count_on;temp3=count_off;

while(temp2>=1)

temp2=temp2-1;while(temp3>=1)

temp3=temp3-1;

t1=temp2*1000;t2=temp3*1000;

if(t1=t2 && t1!=0)

{

count_on=count_on+1-temp2;count_off=count_on-temp3;

}

else{

if(t1!=0){

if(t1>=500)

count_on=count_on+1-temp2;

else

count_on=count_on-temp2;

}

elsecount_on=count_on-temp2;

if(t2!=0)

{if(t2>=500)

count_off=count_off+1-temp3;

elsecount_off=count_off-temp3;

}

elsecount_off=count_off-temp3;

}

ton=0;

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toff=0;}

}

The following expressions check the values of count_on and count_off and make the

decision about the duration of the output in the high position (1) and the low position (0):if(ton==0 && toff==0){

ton=(short)count_on;

toff=(short)count_off;

}else

{

if(ton>0){

output_sample(amp_out);

led_control(0x0x00000000);ton--;

}

else if(toff>0){

output_sample(0);led_control(0x0x07000000);

toff--;

}}

Now we investigate the working of variable amplitude. You are all familiar that the codecis of 16 bits. So,

216 = 65536

You also know that the codec supports the positive as well as negative amplitude value.So,

65536/2=32768

So, from 0 to 32767 is for positive values and the remaining (i.e.; from 32768 to 65535)

is for negative values. You also know that the maximum amplitude that can be inputted

and outputted by the codec is 3V (and 3V). At these values the codec is saturated at32767 (and 32768). So, the following expression calculate the codes for the amplitude

you enter:

amp_out=(short)((amp_in/3)*32767);

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Note: The 0V is represented by 0 and 3V is represented by 32767. Also, the 1V is

represented by 65535 and 3V is represented by 32768.

One last thing to remember is that whenever you turn on or off any of the switch, theprocessor will ask you to enter the duty cycle, amplitude, and frequency for the PWM.


1. C6xdsk.cmd

2. C6xdsk.h

3. C6xinterrupts.h

4. C6xdskinit.h

5. C6xdskinit.c

6. Vectors_11.asm

7. PWM.c

8. Rts6701.lib

9. Switch_read.c

All the files are provided by the Texas except PWM.c and Switch_read.c that are

written by myself.

signal processing manual 2009

Documents