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MATLAB basics

Prof. Dr. M. Krauledat

Faculty of Technology and Bionics

Audio and Speech Processing, Prof. Krauledat

MATLAB Desktop

Command Window

Current Folder Workspace Command

History Help Browser

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Order of precedence

Suggestion: Use parentheses!! Also improves readability.((a*b*c)/(d*e*f))*123 instead of a*b*c/d/e/f*123

MATLAB as Calculator

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MATLAB as Calculator

Test your understanding: Calculate the following expressions

1.

/ .

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MATLAB as Calculator

4 2 2

2

>> ((4+2*2)/2)^2ans =

16

610

13

18

57 59

>> 6*(10/13) + 18/(5*7) + 5 * (9^2)ans =

410.1297

6 35/ 14.

>> 6*35^(1/4)+14^0.35ans =

17.1123

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MATLAB as Calculator

Help-function provides description of the function, e.g. help sin

Detailed documentation is given by doc sin help matlab\elfun provides list of elementary

functions lookfor searches for key words, e.g. lookfor sine Exercise: Find out how to read in audio files into MATLAB

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MATLAB as Calculator

Exercise: Find out how to read in audio files into MATLAB

>> lookfor audio

audioplayer - Audio player object.audiorecorder - Audio recorder object.audiodevinfo - Audio device information.audioplayerreg -audioread - Read audio files>> help audioread

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MATLAB as Calculator

Exercise: 1. Calculate the Nyquist rate for a signal with frequency

content below .2. The frequency threshold is now .

Calculate the Nyquist rate again by using the command history.

3. Save the latest area variable in the file nyquist. Close MATLAB and start it again. Load the file and see if the variable is known.

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Vector- and Matrix-Elements Matrix-oriented approach In MATLAB a vector/matrix is simply an array of scalars

Example: measurement of the temperature once per hour

representation of the data as a vector: [19, 21, 25, 20]

5 5

7

8

5 1 3 5 1 2

8 5 6scalar

Column vector

Row vector

Matrix / array

15

20

25

30

10:00 11:00 12:00 1:00

Temperature

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Vector- and Matrix-Elements

Vectors: To create a row vector, separate the elements by comma or space. Use square brackets. For example,

>>p = [3,7,9]p =

3 7 9

>>p = [3 7 9]p =

3 7 9

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Vector- and Matrix-Elements You can create a column vector by separating the elements by semicolons.

For example,

>>g = [3;7;9]g =

379

You can also create a column vector by using the transpose notation (').

>>p = [3,7,9]'p =

379

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Vector- and Matrix-Elements

Creating Matrices

If the matrix is small you can type it row by row, separating the elements in a given row with spaces or commas and separating the rows with semicolons. For example, typing

>>A = [2,4,10;16,3,7];

creates the following matrix: 2 4 10

16 3 7

Remember, spaces or commas separate elements in different columns, whereas semicolons separate elements in different rows.

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Vector- and Matrix-ElementsFind out how your variables look like!

Command size shows dimensions of the vector/matrix Command length gives the number of elements in the

vector See also workspace

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Initializing with Shortcut Expression

The colon operator (:) easily generates a large vector of regularly spaced elements. Parentheses are not needed but can be used for clarity. Do not use square brackets.

Typing

>>x = m:q:n

creates a vector x of values with a spacing q. Rule of thumb:>>x = first:increment:last

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Exercise

1. Calculate the sine for the angles , , by using shortcut expressions, where Define the angle vector , , Calculate the sine for each angle

2. Consider the function

. We want to assign the

row vector to the variable y.

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Indexing / Addressing

Usage of array indicesMATLAB command Resultb(1) the first element of b in case b contains either

one row or one column.a(1,2) Gives the element on the first row and second

column of a.a(1,:) Gives the first row of a.a(:,3) Gives the third column of a.a(:,2)=[10;10;10] Changes the second column of a into a

column with 10's only. Only works if a is amatrix,

a(1,[3,1]) A matrix consisting of the 3rd and 1st elements of the first row of a.

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Exercise

Considering the 3x3 matrix A=randn(3). Please create/show the numbers by using indexing methods:1. Show 3rd column of the 1st row2. Show 2nd row3. Define a sub-array consisting of numbers from column 1

and 2 and row 1 and 24. Replace 3rd column by ones5. Interchange 2nd and 3rd row

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Element-by-Element OperationSymbol

+

-

+

-

.*

./

.\

.^

Examples

[6,3]+2=[8,5]

[8,3]-5=[3,-2]

[6,5]+[4,8]=[10,13]

[6,5]-[4,8]=[2,-3]

[3,5].*[4,8]=[12,40]

[2,5]./[4,8]=[2/4,5/8]

[2,5].\[4,8]=[2\4,5\8]

[3,5].^2=[3^2,5^2]

2.^[3,5]=[2^3,2^5]

[3,5].^[2,4]=[3^2,5^4]

Operation

Scalar-array addition

Scalar-array subtraction

Array addition

Array subtraction

Array multiplication

Array right division

Array left division

Array exponentiation

Form

A + b

A b

A + B

A B

A.*B

A./B

A.\B

A.^B

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2D Graphics

>> plot(x,y) plots vector y over x x has to be the same size as y If x is not defined, y is plotted over index Example:>> y=[-1 3 5 6 7 3]y =

-1 3 5 6 7 3>> plot(y)

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2D Graphics

>> x=0:0.01:2*pi;>> y=3*cos(2*x);>> plot(x,y)

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2D Graphics

Annotations and Beautifications

grid puts grid lines on the plottitle('mytitle') puts mytitle on top of the plotxlabel('my_xlabel') puts my_xlabel under the horizontal axisylabel('my_ylabel') puts my_ylabel next to the vertical axislegend('one','two') generates a legend with the words one and

two for two plots

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Subplots

>> subplot(m,n,p) Creates several plots in one figure Breaks down the figure into a m-by-n

matrix of plots uses subplot number p as active

plot

Example:>> subplot(2,3,4); >> plot(sin(0:pi/50:2*pi));

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n=3

m=2

p=1 p=2 p=3

p=4 p=5 p=6

MATLAB Script

A script is a sequence of MATLAB instructions Stored in an M-file *.m type displays the content of the script edit opens editor Script can be executed or run by simply entering the name of

the file (w/o .m extension) Search path: Current Folder Documentation: A comment is anything from a % to the end of

the line help command works with scripts as well: first block of

comments will be displayed

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MATLAB ScriptCreating and Using a Script File

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Function User-defined function defined by programmer Can be used either in the command window or in a script Name of the function (functionname) should be the same as the

name of the M-file Local variables General structure:

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Function

Pre-defined structure of a function

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Function

ExampleWrite a function audiostats which takes the number of bits nbits and the sampling rate fs

as input returns the SQNR sqnr and the Nyquist frequency nyfs

for an audio file with the given characteristics.

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Control Flow IF Statement If statement chooses whether another

statement is executed or not (case-by-case-analysis)

General formif logicalexpression1

statementgroup1elseif logicalexpression2

statementgroup2else

statementgroup3end logicalexpression is a

logical/relational expression that is true or false

Action is a statement that will be executed if the logicalexpression is true

Every if statement must have an accompanying end statement. The end statement marks the end of the statements that are to be executed if the logical expression is true.

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Control Flow

Flowchart of a for-end loop

Syntax of a for-end loop

for k = m:s:nend

k: loop index variablem: the value of k in the first passs: the increment in k after each passn: the value of k in the last pass

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Control Flow

ExerciseThe energy of a signal over interval [-N,N] is defined as

Write a script file to compute the signal energy of sin

where N=100.1. Use a for loop to do this.2. Use vector summation and exponentiation.

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Control Flow

Flowchart of the while-loop

Syntaxwhile logical expression

statementsend

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