CS2403 DIGITAL SIGNAL PROCESSING

TWO MARKS QUESTIONS & ANSWER BANK

CLASS: V SEM IT

UNIT – I

SIGNALS AND SYSTEMS

1. What do you meant by the terms: signal and signal processing?

A signal is defined as any physical quantity that varies with time, space, or any other independent variable.

Signal processing is any operation that changes the characteristics of a signal. These characteristics include the amplitude, shape, phase and frequency content of a signal.

2. What are the classifications of signals?

There are five methods of classifying signals based on different features:

(a) Based on independent variable(i) Continuous time signal

(ii) Discrete time signal(b) Depending upon the number of independent variable

(i) One dimensional signal(ii) Two dimensional signal(iii) Multi dimensional signal

(c) Depending upon the certainty by which the signal can be uniquely described as(i) Deterministic signal(ii) Random signal

(c) Based on repetition nature(i) Periodic signal(ii) Non – Periodic signal

(d) Based on reflection(i) Even signal(ii) Odd signal

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3. Define discrete system.

A discrete time system is defined as a device or algorithm that operates on a discrete time input signal x(n), according to some well defined rule, to produce another discrete – time signal y(n) called the output signal.

4. What are the classifications of discrete – time systems?

The classifications of discrete time systems are

1. Static and dynamic system2. Time – variant and time – invariant system3. Linear and non – linear system4. Stable and Un-stable system5. Causal and non-causal system6. IIR and FIR system

5. Differentiate continuous time and discrete time signal.

Continuous time signal: It is also referred as analog signal i.e., the signal is represented continuously in time.

Discrete time signal : Signals are represented as sequence at discrete time intervals .

6. Define digital signal.

A discrete time signal or digital is defined as which discrete values represented by a finite number of digits is referred to as a “digital signal”.

7. What is deterministic signal? Give example.

A signal that can be uniquely determined by a well - defined process such as a mathematical expression or rule, or look-up table is called a deterministic signal.

Example : A sinusoidal signal

8. What is random signal? Give example.

A signal that is generated in a random fashion and cannot be predicted ahead of time is called a “random signal”.

Example: Speech signal, ECG signal and EEG signal.

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9. Define (a) periodic signal (b) non – periodic signal.

Periodic signal: A periodic signal is defined as the signal x(n) is said to be periodic with period N if and only if x( n + N )=x(n) for all n.

Non – periodic signal: A non-periodic signal is defined as if there is no value of N that satisfies the equation x( n + N ) x(n).10. What are the symmetric and antisymmetric signals?

Symmetric signal: A real valued signal x(n) is called symmetric if x(−n) = x(n).

Antisymmetric signal: A signal x(n) is called antisymmetric if x(−n) = − x(n).

11. What are energy and power signals?

Energy signal:

The energy of a discrete time signal x(n) is defined as

A signal x(n) is called an energy signal if and only if the energy obeys the relation. For an energy signal P = 0.

Power signal: The average power of a discrete time signal x(n) is defined as

.

A signal x(n) is called power signal if and only if the average power P satisfies the condition .

12. What are the different types of signal representation?

The different types of signal representation are

(i) Graphical representation (ii) Functional representation(iii) Tabular representation (iv) Sequence representation

13. What are the different types of operations performed on discrete – time signals?

The different types of operations performed on discrete – time signals are

(1) Delay of a signal(2) Advance of a signal(3) Folding or Reflection of a signal

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(4) Time scaling(5) Amplitude scaling(6) Addition of signals

(7) Multiplication of signals.

14. Represent the following duration sequence x(n) = { 1, 3, −1, −4 } as a sum of weighted impulse sequences.

Given x(n) = { 1, 3, −1, − 4 }

We can write

Therefore sum of weighted impulse signal is .

15. What is a static and dynamic system?

A discrete –time system is called static or “memory less” if its output at any instants ‘n’ depends on the input samples at the same time, but not an past or future samples of the input.

Ex., y(n) = ax(n) y(n)=ax2(n)

In any other case, the system is said to be dynamic or to have memory.

Ex., y(n) = ax(n - 1) + x(n - 2) y(n) = x(n) + x(n - 1)

16. What is a time – invariant system?

A system is called time – invariant if its input – output characteristics do not change with time.

Ex., y(n) = x(n) + x(n -1)

17. What is a causal system?

A system is said to be causal if the output of the system at any time n depends only on present and past inputs, but does not depend on future inputs.

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This can be expressed mathematically as,y(n) = F[x(n), x(n -1), x(n - 2)………]

18. Define a stable system.

Any relaxed system is said to be bounded input-bounded output (BIBO) stable if and only if every bounded input yields a bounded output. Mathematically, their exist some finite numbers, Mx and My such that,

19. What is a linear system?

A system that satisfies the superposition principle is said to be a linear system. Superposition principle states that, the response of the system to a weighted sum of signals be equal to the corresponding weighted sum of the outputs of the system to each of the individuals input signals.20. Define unit sample response (impulse response) of a system and what are its significance?

The unit sample response is defined as the output signal designated as h(n), obtained from a discrete – time system when the input signal is a unit sample sequence (unit impulse).

The output y(n) of an LTI system for an input signal x(n) can be obtained by convolution of the impulse response h(n) and the input signal x(n).

21. What is the causality condition for an LTI system?

The necessary and sufficient condition for causality of an LTI system is, its unit sample response h(n) = 0 for negative values of n i.e.,

h(n) = 0 for n < 0

22. What is the necessary and sufficient condition on the impulse response for stability?

The necessary and sufficient condition guaranteeing the stability of a linear time-invariant system is that its impulse response is absolutely summable.

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.

23. What is meant by discrete or linear convolution?

The convolution of discrete – time signal is known as discrete convolution. Let x(n) be the input to an LTI system and y(n) be the output of the system. Let h(n) be the response of the system to an impulse. The output y(n) can be obtained by convolving the impulse response h(n) and the input signal x(n).

24. What are the steps involved in the convolution process?

The steps involved in the convolution process are

1. Express both sequences in terms of the index k.2. Folding: Fold the h(k) about the origin and obtain h(-k).3. Time shifting : Shift the h(k) by n units to right if n is positive or left if n is negative to obtain h(n-k).4. Multiplication: Multiply x(k) by h(n-k) to obtain w(k)=x(k)h(n-k)5. Summation: Sum all the values of the product w(k) to obtain the value of output y(n).6. Increment the index n, shift the sequence h(n-k) to right by one

sample and do step4.

25. What do you mean by sampling process?

Sampling is the conversion of a continuous – time signal (or analog signal) into a discrete – time signal obtained by taking samples of the continuous time signal (or analog signal) at discrete time instants.

26. State sampling theorem.

A sampling theorem states that in the band limited continuous time signal with highest frequency (band width) fm in hertz , can be uniquely recovered from its

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samples provided that the sampling rate fs is greater than or equal to 2fm samples per second.

27. Define Nyquist rate.

The Nyquist rate is defined as the frequency 2fm , which, under sampling theorem, must be exceeded by the sampling frequency.

28. What is meant by quantization process?

The process of converting a discrete time continuous valued signal into discrete time discrete valued signal is called quantization.

29. What is aliasing effect?

The superimposition of high frequency component on the low frequency is known as “frequency aliasing” or “aliasing effect”.

30. How can aliasing be avoided?

To avoid aliasing the sampling frequency must be greater than twice the highest frequency present in the signal.

31. What is an anti aliasing filter?

A filter used to reject frequency signals before it is sampled to reduce the aliasing is called an anti aliasing filter.

32. What is meant by critical sampling?

If the sampling frequency is exactly equal to the Nyquist rate then the sampling frequency is known as critical sampling.

33. What are the steps involved in the A/D conversion?

The steps involved in the A/D conversion are1. Sampling2. Quantization3. Coding (each discrete value is represented by a binary sequence)

34. What is meant by quantization error?

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Quantization error is the difference between the quantized value and actual sample value.

eq(n) = xq(n) - x(n)

35. What is a quantization level?

Quantization level is the value that allows in a digital signal is called the quantization level.

36. Define resolution or quantization step size.

The resolution is defined as the distance between two successive level.

37. What is SQNR?

The quality of the output of the A/D converter is usually measured by the Signal to Quantization Noise Ratio (SQNR) , which is ratio of the signal power to noise power.

38. What is the use of a Sample and Hold circuit?

The sample and hold circuit is used to hold the sample the analog signal and hold the sampled value constant as long as the A/D converter takes time for accurate conversion.

39. Define conversion time.

Conversion time may be defined as the time taken by an ADC for converting a given amplitude, expressed in decimal value, of a quantized analog signal applied across its input terminals into corresponding binary – equivalent value.

40. Define voltage resolution.

The voltage resolution is defined as

where – full scale voltage and

n – number of bits41. Define percentage resolution.

Percentage resolution is defined as

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wheren – number of bits

42. What are the advantages and disadvantages of counter – ramp type ADCs?

Advantages of counter – ramp type ADCs are

1. The principle is simple and straightforward2. It is very easy to construct this ADC3. This basic principle is employed in many advanced ADCs

Disadvantages of counter – ramp type ADCs are

1. Only increasing voltages can be measured2. The system is very slow3. This may be mainly used to read DC voltages4. Practically the system comes to rest only when Vd > Va . This set an

error in readings

43. What are the advantages and disadvantages of SAADC?

Advantages of SAADC are

1. It is more accurate than the stair case ( counter ramp ) ADC2. It maintains a high resolution3. It is much faster4. Its conversion time is much less

Disadvantages of SAADC are

1. It requires a complex register called the successive approximation register

2. It is costly, as it contains more components

44. Write down the formula for conversion time of SAADC?

wheren – number of bits andf – clock frequency

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45. What are the advantages and disadvantages of Flash converter?

Advantages of flash converter are

1. The fastest conversion process (governed only by propagation delay of the gates)

2. Highest accuracy3. Highest resolution possible by increasing the number of comparators.

Disadvantages of flash converter are

1. Very complicated circuitry2. Cost is proportional to the number of comparators, which in turn

depends on the resolution required

46. What are the different types of analog to digital converters?

The different types of analog to digital converters are

1. Flash A/D converter2. Successive approximation converter3. Counting type A/D converter4. Over sampling Sigma – Delta converter

47. What are the different types of digital to analog converter?

The different types of digital to analog converters are

1. Weighted – resistor D/A converter2. Resistor – ladder D/A converter3. Over sampling D/A converter

48. Define Z – transform.

The Z –transform of a discrete – time signal or sequence is defined as the power series.

49. What is meant by region of convergence?

The Region Of Convergence (ROC) of X(z) is the set of all values of z for which X(z) attains a finite value.

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50. What are the properties of region of convergence?

The properties of region of convergence are

1. The ROC is a ring or disk in the Z – plane centered at the origin2. The ROC cannot contains any poles3. The ROC of an LTI stable system contains the unit circle4. The ROC must be a connected region

51. What are the properties of Z - transform?

1. Linearity: Z

2. Shifting: (a)

(b)

3. Multiplication:

4. Scaling in z- domain:

5. Time reversal :6. Conjugation:

7. Convolution:

8. Initial value:

9. Final value:

52. State Parseval’s relation in Z - transform. Parseval’s relation in Z - transform state that

If x1(n) and x2(n) are complex valued sequences, then

53. What is the relationship between z-transform and DTFT?

The z-transform of x(n) is given by …….(1)

where

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Substituting z value in equation (1) we get,

…………………..(2)

The Fourier transform of x(n) is given by

……………………….(3)

Equation (2) and equation (3) are identical, when r = 1. In the Z - plane this corresponds to the locus of points on the unit circle . Hence is equal to X(z) evaluated along unit circle, or

For to exist, the ROC of X(z) must include the unit circle.

54. What are the different methods of evaluating inverse z – transform?

1. Long division method.2. Partial fraction method.3. Residue method.4. Convolution method.

55. Find the convolution of the following using z- transform.

Solution:

56. Define system function.Let x(n) and y(n) be the input and output sequences of an LTI system with

impulse response h(n). Then the system function of the LTI system is defined as the ratio of Y (z) and X (z), i.e.,

where,Y(z) is the z – transform of the output signal y(n)X(z) is the z – transform of the input signal x(n)

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UNIT – II

FAST FOURIER TRANSFORM

1. Define Fourier transform of a discrete time signal.

The Fourier transform of a discrete time signal x(n) is defined as

2. Why FT of a discrete time signal is called signal spectrum?

By taking Fourier transform of a discrete time signal x(n) , it is decomposed into its frequency components . Hence the Fourier transform is called signal spectrum.

3. List the difference between Fourier transform of discrete time signal and analog signal.

i) The FT of analog signal consists of a spectrum with a frequency range But the FT of discrete time signal is unique in the range

, and also it is periodic with periodicity of 2 .

ii) The FT of analog signals involves integration but FT of discrete time signals involves summation.

4. Define inverse Fourier transform.

The inverse Fourier transform of X() is defined as

5. Give some applications of Fourier transform.

The applications of Fourier transform are

1. The frequency response of LTI system is given by the Fourier transform of the impulse response of the system.

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2. The ratio of the Fourier transform of output to Fourier transform of input is the transfer function of the system in frequency domain.

3. The response of an LTI system can be easily computed using convolution property of Fourier transform.

6. What is the frequency response of LTI system?

The Fourier transform of the impulse response h(n) of the system is called frequency response of the system. It is denoted by H().

7. Write the properties of frequency response of LTI system.

The properties of frequency response of LTI system are

i) The frequency response is periodic function with a period of 2 .

ii) If h(n) is real then is symmetric and is antisymmetric.

iii) If h(n) is complex then the real part of is antisymmteric over the interval .

iv) The frequency response is a continuous function of .

8. Write short notes on the frequency response of first order system.

A first order system is characterized by the difference equation

The frequency response of first order system depends on the co efficient “a” in the difference equation governing the LTI system. When the value of “a|” is in the range of 0<a<1, the first order system behave as a low pass filter. When the value of “a” is in the range –1<a<0, the first order system behave as a high pass filter.

9. Write a short note on the frequency response of second order system.

A second order system is characterized by the difference equation

The frequency response of second order system depends on the parameters

“r” and “ ” in the difference equation the LTI system. When the value of r is in

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the range of 0<r<1, the second order system behave as a resonant filter with center frequency . When the value of r is varied from 0 to 1 , the sharpness of resonant peak increases.

10. Define discrete Fourier series.

Consider a sequence xp(n) with a period of N samples so that xp(n) = xp(n/N); Then the discrete Fourier series of the sequence xp(n) is defined as

11. What are the two basic differences between the Fourier transform of a discrete time signal with the Fourier transform of a continuous time signal?

1. For a continuous signal, the frequency range extends from On the other hand, the frequency range of a discrete – time signal extends from

.

2. The Fourier transform of a continuous signal involves integration, whereas, the Fourier transform of a discrete – time signal involves summation process.

12. Find the Fourier transform of a sequence x(n) = 1 for

= 0 otherwise.Solution:

13. Define the Discrete Fourier transformation of a given sequence x(n).

The N- point DFT of a sequence x(n) is

k= 0, 1, 2……..N-1.

14. Write the formula for N- point IDFT of a sequence X(k).

The N-point IDFT of a sequence X(k) is

n= 0, 1 , 2 …..N-1 .

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15. List any four proerties of DFT.

(a) Periodicity

If X(k) is N- point DFT of a finite duration sequence x(n)then

(b) LinearityIf X1(k) = DFT[x1(n)] and X2(k) = DFT[x2(n)]then DFT[a1x1(n)+a2x2(n)]=a1X1(k)+a2x2(k)

(c) Time reversal of a sequenceIf DFT {x(n)} = X(k),then DFT{x((-n))N} = DFT{x(N-n)} = X((-k))N = X(N-k)

(d) Circular time shifting of a sequenceIf DFT {x(n)}= X(k),then DFT{x((n-l))N} = X(k)

42. IF N-point sequence x(n) has N- point DFT X(k) then what is the DFT of the following?

Solution:

43. Calculate the DFT of the sequence x(n) =

Solution:

K=0, 1 , 2…..N-1

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18. State the time shifting property of DFT.

The time shifting properties of DFT states that

If DFT[x(n)] = X(k), then

DFT[x((n-m))N] =

19. Find the DFT of the sequence x(n) = { 1,1,0,0 }

Solution:

; k = 0,1,2,…..N-1.

20. When the DFT X(k) of a sequence x(n) is imaginary?

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If the sequence x(n) is real and odd (or) imaginary and even, then X(k) is purely imaginary.

21. When the DFT X(k) of a sequence x(n) is real?

If the sequence x(n) is real and even (or) imaginary and odd , then X(k) is purely real.

22. State Circular frequency shifting property of DFT. The circular frequency shifting property of DFT states that

If DFT[x(n)]=X(k),

ThenDFT[x(n)

23. What is zero padding? What are its uses?

The process of lengthening the sequence by adding zero – valued samples is called appending with zeros or zero – padding.

USES:(i) We can get “better display” of the frequency spectrum.(ii) With zero padding, the DFT can be used in linear filtering.

24. What do you understand by periodic convolution?

Let and be two periodic sequences each with period N with

……………………………(1)

then the periodic sequence with Fourier series coefficients can be obtained by periodic convolution, defined as

………………………………(2)

The convolution in the form of equation (2) is known as periodic convolution, as the sequences in equation (2) are all periodic with period N, and the summation is over one period.

25. Define circular convolution.

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The convolution property of DFT is defined as the multiplication of the DFTs of the two sequence is equivalent to the DFT of the circular convolution of the two sequences.

26. How the circular convolution is obtained by using Graphical method?

Given two sequences and , the circular convolution of these two sequences can be obtained by using the following steps.

1. Graph N samples of , as equally spaced points around an outer circle in counter clockwise direction.

2. Start at the same point as graph N samples of as equally spaced points around an inner circle in clock wise direction.

3. Multiply corresponding samples on the two circles and sum the products to produce output.

4. Rotate the inner circle one sample at a time in clock wise direction and go to step3 to obtain the next value of output.

5. Repeat step4 until the inner circle first sample lines up with the first sample of the exterior circle once again.

27. Distinguish between linear and circular convolution of two sequences.

Sl.NO Linear Convolution Circular convolution1. If x(n) is a sequence of L number of

samples and h(n) with M number of samples , after convolution y(n) will contain N=L+M-1

If x(n) is a sequence of L number of samples and h(n) with M number of samples , after convolution y(n) will contain N=Max(L,M) samples.

2. Linear convolution can be used to find the response of a linear filter.

Circular convolution cannot be used to find the response of a filter.

3. Zero padding is not necessary to find the response of a linear filter.

Zero padding is necessary to find the response of a filter.

28. What are the steps involved in circular convolution?

The circular convolution involves basically four steps as the ordinary linear convolution. These are

1. Folding the sequence2. Circular time shifting the folded sequence

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3. Multiplying the two sequences to obtain the product sequence.4. Summing the values of product sequence.

29. What are the different methods performing circular convolution?

1. Graphical method2. Stockhman’s method3. Tabular array method4. Matrix method.

30. Obtain the circular convolution the following sequencesx(n)={1, 2, 1 }; h(n)={ 1, -2, 2 }

Solution:

The circular convolution of the above sequences can be obtained by using matrix method.

31. How will you obtain linear convolution from circular convolution.

Consider two finite duration sequences x9n) and h(n0 of duration L samples and N samples respectively. The linear convolution of these two sequences produces an output sequence of duration L+M-1 samples , whereas , the circular convolution of x(n) and h(n) give N samples where N=Max(L,M) . In order to obtain the number of samples in circular convolution equal to L+M-1, both x(n) and h(n) must be appended with appropriate number of zero valued samples. In other words, by increasing the length of the sequences x(n) and h(n) to L+M-1 points and then circularly convolving the resulting sequences we obtain the same result as that of linear convolution.

32. What is meant by sectioned convolution?

If the data sequence x(n) is of long duration , it is very difficult to obtain the output sequence y(n) due to limited memory of a digital computer. Therefore, the data sequence is divided up into smaller section. These sections are processed separately one at a time and combined later to get the output.

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33. What are the different methods used for the sectioned convolution?

The two methods used for the sectioned convolution are (i)the overlap-add method (ii)Over lap-save method.

34. Differentiate (i) overlap-add method (ii) overlap – save method.

Sl.No Overlap – add method Overlap – save method1. In this method the size of the input

data block is N=L+M-1In this method the size of the input data block is L.

2. Each data block consists of the last M-1 data points of the previous data followed by the L new data points.

Each data block is L points and we appended M-1 zeros to compute N-point DFT.

3. In each output block M-1 points are corrupted due to aliasing, as circular convolution is employed.

In this no corruption due to aliasing as linear convolution is performed using circular convolution.

4. To form the output sequence the first M-1 data points are discarded in each output block and the remaining datas are fitted together.

To form the output sequence, the last M-1 points from each output block is added to the first (M-1) points of the succeeding block.

35. Distinguish between DFT and DTFT.

Sl.No DFT DTFT1. Obtained by performing sampling

operation in both the time and frequency domains.

Sampling is performed only in time domain.

2. Discrete frequency spectrum Continuous function of

36. What is FFT?

The term Fast Fourier Transform (FFT) usually refers to a class of algorithms for efficiently computing the DFT.It makes use of the symmetry and periodicity properties of twiddle factor to effectively reduce the DFT computation time.It is based on the fundamental principle of decomposing the computation of DFT of a sequence of length N into successively smaller discrete Fourier transforms. The FFT algorithm provides speed increase factors, when compared with direct computation of the DFT, of approximately 64 and 205 for 256 points and 1024 – point transforms respectively.

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37. How many multiplications and additions are required to compute N-point DFT using radix-2 FFT?

The number of multiplications and additions required to compute N-point DFT

using radix-2 FFT are respectively.

38. How many multiplications and additions are required to compute N-point DFT directly?

The number of multiplications and additions required to compute N-point DFT u are respectively.

39. What is the speed improvement factor in calculating 64 – point DFT of a sequence using direct computation and FFT algorithms?

(or)Calculate the number of multiplications needed in the calculation of DFT and FFT with 64-point sequence.

The number of complex multiplications required using direct computation is

The number of complex multiplications required using FFT is

Speed improvement factor=

40. What is meant by radix-2 FFT?

The FFT algorithm is most efficient in calculating N-point DFT. If the number of output points N can be expressed as a power of 2, that is where m is an integer, and then this algorithm is known as radix – 2 FFT algorithms.

41. What is decimation – in – time algorithm?

The computation of 8 – point DFT using radix-2 FFT, involves three stages of computations. Here N=8=23, therefore r=2 and m=3.

The given 8 – point sequence is decimated to 2- point sequences. For each 2 – point sequence, the 2-popint DFT is computed. From the result of 2 – point DFT the 4 – point DFT can be computed. From the result of 4-point DFT, the 8 – point DFT can be computed.

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42. What is decimation in frequency algorithm?

It is the popular form of the FFT algorithm. In this the output sequence X(k) is divided into smaller and smaller subsequences, that is why the name decimation in frequency.

43. What are the difference between and similarities between DIT and DIF algorithms?

Difference between DIT and DIF:

1) In DIT, the input is bit-reversed while the output is in natural order. For DIF, the reverse is true, i.e., input is normal order, while the output bit is reversed. However, both DIT and DIF can go from normal to shuffled data or vice versa.

2) Considering the butterfly diagram, in DIF, the complex multiplication takes place after the add – subtract operation

Similarities between DIT and DIF:

1) Both algorithms require same number of operations to compute DFT.

2) Both algorithms require bit – reversal at some place during computation.

44. What are the applications of FFT algorithms?

The applications of FFT algorithms includes

(i) Linear filtering(ii) Correlation (iii) Spectrum analysis

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UNIT – III

IIR FILTER DESIGN

1. What are the different types of structures for realization of IIR systems?

The different types of structures for realization of IIR system are

(i) Direct form I structure (ii) Direct form II structure(iii) Cascade form structure (iv) Parallel form structure(v) Lattice – ladder form structure.

2. Distinguish between recursive realization and non-recursive realization.

For recursive realization the current output y(n) is a function of past outputs, past and present inputs. This form corresponds to an Infinite – Impulse response (IIR) digital filter.

For non-recursive realizations current output sample y(n) is a function of only past and present inputs. This form corresponds to a Finite Impulse response (FIR) digital filter.

3.How many number of additions, multiplications and memory locations are required to realize a system H(z) having M zeros and N poles in (a) Direct form – I realization (b) Direct form – II realization.

(a) The Direct form – I realization requires M+N+1 multiplications, M+N additions and M + N + 1 memory locations.

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(b) The Direct form – II realization requires M+N+1 multiplication, M+N additions and the maximum of (M, N) memory locations.

4. What is the main advantage of Direct form- II realizations when compared to Direct form –I realization?

In Direct form – II realization, the number of memory locations required is less than that of Direct form – I realization.

5. Define signal flow graph.

A signal flow graph is defined as a graphical representation of the relationship between the variables of a set of linear difference equations.

6. What is transposed theorem and transposed structure?

The transpose of a structure is defined by the following operations.

(i)Reverse the directions of all branches in the signal flow graph(ii) Interchange the input and outputs(iii)Reverse the roles of all nodes in the flow graph(iv)Summing points become branching points(v) Branching points become summing points

According to transposition theorem if we reverse the directions of all branch transmittance and interchange the input and output in the flow graph, the system function remains unchanged.

7. What is Canonic form structure?

The Direct form –II realization requires minimum number of delays for the realization of the system. Hence it is called as “Canonic form” structure.

8. What is the main disadvantage of direct form realization?

The Direct form realization is extremely sensitive to parameter quantization. When the order of the system N is large, a small change in a filter coefficient due to parameter quantization, results in a large change in the location of the poles and zeros of the system.

9. What is the advantage of cascade realization?

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Quantization errors can be minimized if we realize an LTI system in cascade form.

10. What are the different types of filters based on impulse response?

Based on impulse response the filters are of two types

1. IIR filter2. FIR filter

The IIR filters are of recursive type, whereby the present output sample depends on the present input, past inputs samples and output samples.

The FIR filters are of non recursive type whereby the present output sample is depends on the present input sample and previous input samples.

11.What is the general form of IIR filter?

The most general form of IIR filter can be written as

12. Give the magnitude of Butterworth filter. What is the effect of varying order of N on magnitude and phase response?

The magnitude function of the Butterworth filter is given by

Where N is the order of the filter and is the cut off frequency. The magnitude response of the Butterworth filter closely approximates the ideal response as the orderN increases. The phase response becomes more non-linear as N increases.

13. Give any two properties of Butterworth lowpass filters.

1. The magnitude response of the Butterworth filter decreases monotonically as the frequency increases from 0 to α

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2. The magnitude response of the Butterworth filter closely approximates the ideal response as the order N increases

3. The Butterworth filters are all pole designs4. The poles of the Butterworth filter lies on a circle5. At the cut off frequency , the magnitude of normalized Butterworth filter is

14. What is Butterworth approximation?

In Butterworth approximation, the error function is selected such that the magnitude is maximally flat in the origin (i.e., at =0) and monotonically decreasing with increasing .

15. How the poles of Butterworth transfer function are located in s- plane?

The poles of the normalized Butterworth transfer function symmetrically lies on

a unit circle in s-plane with angular spacing of .

16. What is Chebyshev approximation?

In Chebyshev approximation, the approximation function is selected such that the error is minimized over a prescribed band of frequencies.

17. What is Type –1 Chebyshev approximation?

In type –1 Chebyshev approximation, the error function is selected such that, the magnitude response is equiripple in the pass band and monotonic in the stop band.

18. What is Type –2 Chebyshev approximation?

In type –2 Chebyshev approximation, the error function is selected such that, the magnitude response is monotonic in pass band and equiripple in the stop band. The Type -2 magnitude response is called inverse Chebyshev response.

19. Write the magnitude function of Chebyshev lowpass filter.

The magnitude response of Type -1 lowpass Chebyshev filter is given by

27

where is attenuation constant and

is the Chebyshev polynomial of the first kind of degree N

20. How the order of the filter affects the frequency response of Chebyshev filter.

From the magnitude response of Type -1 Chebyshev filter it can be observed that the magnitude response approaches the ideal response as the order of the filter is increased.

21. How will you determine the order N of Chebyshev filter.

The order N of the Chebyshev filter is given by

where

22. What are the properties of Chebyshev filter?

The properties of Chebyshev filters are

1. The magnitude response of the Chebyshev filter exhibits in ripple either in pass band or in the stop band according to the type

2. The magnitude response approaches the ideal response as the value of N increases

3. The Chebyshev type – 1 filter are all pole designs4. The poles of Chebyshev filter lies on an ellipse

5. The normalized magnitude function has a value of at the cutoff

frequency23. Compare the Butterworth and Chebyshev Type -1 filter.

Sl.No Butterworth filter Chebyshev filter1. All pole design All pole design

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2. The poles lie on a circle in s-plane The poles lie on a ellipse in s-plane3. The magnitude response is

maximally flat at the origin and monotonically decreasing function of .

The magnitude response is equiripple in pass band and monotonically decreasing in the stop band.

4. The normalized magnitude

response has a value of at the

cut off frequency .

The normalized magnitude response has a

value of at the cut off frequency

.5. Only few parameters have to be

calculated to determine the transfer function.

A large number of parameter has to be calculated to determine the transfer function.

24. What are the different types of filters based on the frequency response?

The filters can be classified based on frequency response. They are (i) low pass filter (ii)high pass filter (iii)Band pass filter and (iv)Band reject filter.

25. Distinguish between FIR and IIR filter.

Sl.No FIR filter IIR filter1. These filters can be easily

designed to have perfectly linear phase.

These filters do not have linear phase.

2. FIR filters can be realized recursively and non – recursively.

IIR filters are easily realized recursively.

3. Greater flexibility to control the shape of their magnitude response.

Less flexibility, usually limited to specific kind of filters.

4. Error due to round off noise is less severe in FIR filters, mainly because feedback is not used.

The round off noise in IIR filters is more.

26. What are the design techniques of designing FIR filters?

These are three well-known methods for designing FIR filters with linear phase. These are (1) Windows method (2) Frequency sampling method (3) Optimal or minimax design.

27. What do you understand by linear phase response?

For a linear phase filter . The linear phase filter did not alter the shape of the original signal. If the phase response of the filter is non linear the output

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signal may be distorted one. In many cases a linear phase characteristic is required throughout the passband of the filter to preserve the shape of a given signal with in the pass band. IIR filter cannot produce a linear phase. The FIR filter can give linear phase, when the impulse response of the filter is symmetric about its mid point.

28. For what kind of application, the antisymmetrical impulse response can be used?

The antisymmetrical impulse response can be used to design Hilbert transformers and differentiators.

29. For what kind of application, the symmetrical impulse response can be used?

The impulse response, which is symmetric having odd number of samples can be used to design all types of filters, i.e., lowpass, highpass, bandpass and bandreject.

The symmetric impulse response having even number of samples can be used to design lowpass and bandpass filter.

30. How can you design digital filters from the analog filters?

The designs of analog filters to digital filters are

1. Map the desired digital filter specifications into those for an equivalent analog filter

2. Derive the analog transfer function for the analog prototype3. Transform the transfer function of the analog prototype into an equivalent

digital filter transfer function

31. Mention any two procedures for digitizing the transfer function of an analog filter.

The two important procedures for digitizing the transfer function of an analog filter are

1. Impulse invariance method2. Bilinear transformation method

32. What are the requirements for a digital filter to be stable and causal?

The requirements of digital filter to be stable and causal are

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i. The digital transfer function H(z) should be a rational function of z and the co-efficient of z should be real

ii. The poles should lie inside the unit circle in z-planeiii. The number of zeros should be less than or equal to number of poles

33. What are the requirements for a analog filter to be stable and causal?

The requirements of analog filter to be stable and causal are

i. The digital transfer function Ha(s) should be a rational function of s and the co-efficient of s should be real

ii. The poles should lie on the left half of s-planeiii. The number of zeros should be less than or equal to number of poles

34. What are the advantages and disadvantages of digital filters?

The advantages of digital filters are

1. High thermal stability due to absence of resistors, inductors and capacitors

2. The performance characteristics like accuracy, dynamic range, stability and tolerance can be enhanced by increasing the length of the registers

3. The digital filters are programmable

4. Multiplexing and adaptive filtering are possible

The disadvantages of digital filters are

1. The bandwidth of the discrete signal is limited by the sampling frequency

2. The performance of the digital filter depends on the hardware used to implement the filter

35. What is impulse invariant transformation?

The transformation of analog filter to digital filter without modifying the impulse response of the filter is called impulse invariant transformation (i.e., in this transformation the impulse response of the digital filter will be sampled version of the impulse response of the analog filter.)

36. What is the main objective of impulse invariant transformation?

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The objective of this method is to develop an IIR filter transfer function whose impulse is the sampled version of the impulse response of the analog filter. Therefore the frequency response characteristics of the analog filter are preserved.

37. Write the impulse invariant transformation used to transform real poles with and without multiplicity.

The impulse invariant transformation used to transform real poles (at s = - pi) without multiplicity is

The impulse invariant transformation used to transform multiple real pole (at s = - pi) is

38. What is the relation between digital and analog frequency in impulse invariant transformation?

The relation between analog and digital frequency in impulse invariant transformation is given by

Digital frequency,

Where, - Analog frequency and

- Sampling time period

39. What is Bilinear transformation?

The Bilinear transformation is a conformal mapping that transforms the s-plane to z-plane . In this mapping the imaginary axis of s-plane is mapped into the unit circle in z-plane, the left half of s-plane is mapped into interior of unit circle in z-plane and the right half of s-plane is mapped into exterior of unit circle in z-plane . The Bilinear mapping is a one – to-one mapping and it is accomplished when

40. What is the relation between digital and analog frequency in Bilinear transformation?

In Bilinear transformation , the digital frequency and analog frequency are related by the equation,

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Digital frequency, or

Analog frequency

where, - Analog frequency

- Sampling time period

41. What is frequency warping?

In bilinear transformation the relation between analog and digital frequencies is nonlinear. When the s-plane is mapped into z-plane using bilinear transformation, this nonlinear relationship introduces distortion in frequency axis, which is called frequency warping.

42. What is prewarping? Why it is employed?

In IIR filter design using bilinear transformation, the conversion of the specified digital frequencies to analog frequencies is called prewarping.

The prewarping is necessary to eliminate the effect of warping on amplitude response.

43. Explain the technique of prewarping.

In IIR filter design using bilinear transformation the specified digital frequencies are converted to analog equivalent frequencies, which are called prewarp frequencies. Using the prewarp frequencies, the analog filter transfer function is designed and then it is transformed to digital filter transfer function.

44. Compare the impulse invariant and bilinear transformations.

Sl.No Impulse Invariant transformation Bilinear transformation1. It is many – to – one mapping It is one – to – one mapping.

2. The relation between analog and digital frequency is linear.

The relation between analog and digital frequency is nonlinear.

3. To prevent the problem of aliasing the analog filters should be band limited.

There is no problem of aliasing and so the analog filter need not be band limited.

The magnitude and phase response of Due to the effect of warping, the phase

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4. analog filter can be preserved by choosing low sampling time or high sampling frequency.

response of analog filter cannot be preserved. But the magnitude response can be preserved by prewarping.

UNIT – IV

FIR FILTER DESGIN

1. What is the condition for the impulse response of FIR filter to satisfy for constant group and phase delay and for only constant group delay?

For linear phase FIR filter to have both constant group delay and constant phase delay.

For satisfying above condition

that is the impulse response must be symmetrical about

If one constant group delay is desired then

For satisfying the above condition

that is the impulse response must be antisymmetrical about

2. What are the properties of FIR filter? The properties of FIR filters are

1. FIR filter is always stable because all its poles are at the origin.2. A realizable filter can always be obtained.3. FIR filter has a linear phase response.

3. What are the steps involved in the FIR filter design?

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The steps involved in the FIR filter design are

i) Choose the desired (ideal) frequency responseii) Take inverse Fourier transform of to getiii) Convert the infinite duration to a finite duration sequenceiv) Take Z – transform of to get the transfer function of the FIR

filter

4. What is the necessary and sufficient condition for the linear phase characteristic of a FIR filter?

The necessary and sufficient condition for the linear phase characteristic of a FIR filter is that the phase function should be a linear function of , which in turn requires constant phase delay or constant group delay.

5. How the constant group delay and phase delay is achieved in linear phase FIR filters.

Frequency response of FIR filters with constant group and phase delay

The following conditions have to be satisfied to achieve constant group and phase delay.

Phase delay, (i.e., phase delay is constant)

Group delay, (i.e., group delay is constant)

Impulse response, h(n) = - h( N -1 – n ) (i.e., impulse response is anti symmetric)

6. What are the possible types of impulse response for linear phase FIR filters?

There are four types of impulse response for linear phase FIR filters

1. Symmetric impulse response when N is odd.2. Symmetric impulse response when N is even.3. Antisymmetric impulse response when N is odd.4. Antisymmetric impulse response when N is even.

7. List the well known design techniques for linear phase FIR filter.

35

There are three well known methods of design techniques for linear phase FIR filters. They are,

i) Fourier series method and window methodii) Frequency sampling methodiii) Optimal filter design method

8. Write the two concepts that lead to the Fourier series or window method of designing FIR filters.

The following two concepts lead to the design of FIR filters by Fourier series method.

i. The frequency response of a digital filter is periodic with period equal to sampling frequency

ii. Any periodic function can be expressed as a linear combination of complex exponentials

9. Write the procedure for designing FIR filter by Fourier series method.

The procedure for designing FIR filter by Fourier series method is

i) Choose the desired (ideal) frequency response of the filterii) Evaluate the Fourier series co-efficient of which gives the desired

impulse response

iii) Truncate the infinite sequence to a finite duration sequence

iv) Take Z – transform of to get a noncausal filter transfer function of the FIR filter

v) Multiply by to convert noncausal transfer function to a

realizable causal FIR filter transfer function

10. What are the disadvantages of Fourier series method?

36

In designing FIR filter using Fourier series method the infinite duration impulse

response is truncated at n= . Direct truncation of the series will lead to fixed

percentage overshoots and undershoots before and after an approximated discontinuity in the frequency response.

11. What is Gibbs phenomenon?

One possible way of finding an FIR filter that approximates

would be to truncate the infinite Fourier series at n = .The abrupt truncation

of the series will lead to oscillation both in passband and in stopband. This phenomenon is known as Gibbs phenomenon.

12. Write the procedure for designing FIR filter using windows.

The procedure for designing FIR filter using windows are

i) Choose the desired (ideal) frequency response of the filterii) Evaluate the Fourier series co-efficient of which gives the

desired impulse response

iii) Choose a window sequence w(n) and multiply the infinite sequence by w(n)to convert the infinite duration impulse response to

finite duration impulse response

iv) Find the transfer function of the realizable FIR filter

13. What are the desirable characteristics of the window?

The desirable characteristics of the window are

1. The central lobe of the frequency response of the window should contain most of the energy and should be narrow

2. The highest side lobe level of the frequency response should be small

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3. The side lobe of the frequency response should decrease in energy rapidly as tends to

14.What is window and why it is necessary?

One possible way of finding an FIR filter that approximates

would be to truncate the infinite Fourier series at n= . The abrupt

truncation of the series will lead to oscillation both in passband and in stopband. These oscillations can be reduced through the use of less abrupt truncation of the Fourier series. This can be achieved by multiplying the infinite impulse response with a finite weighing , called a window.

15. List characteristics of FIR filter designed using windows.

The characteristics of FIR filter designed using windows are

i) The width of the transition band depends on the type of windowii) The width of the transition band can be made narrow by increasing the value of N where N is the length of the window sequenceiii) The attenuation in the stop band is fixed for a given window, except in case of Kaiser window where it is variable

16. Write the procedure for FIR filter design by frequency sampling method.

The procedures for FIR filter design by frequency sampling method are

1. Choose the desired frequency response 2. Take N – samples of to generate the sequence 3. Take inverse DFT of to get the impulse response h(n)4. The transfer function H(z) of the filter is obtained by taking Z – transform of

impulse response

17. What is meant by Optimum equiripple design criterion? Why it is followed?

In FIR filter design by Chebyshev approximation technique, the weighted approximation error between the desired frequency and the actual frequency

38

response is spread evenly across the passband and stopband.The resulting filter will have ripples in both the passband and stopband. This concept of design is called optimum equiripple design criterion.

The optimum equiripple criterion is used to design FIR filter in order to satisfy the specifications of passband and stopband.

18.Write the expression for frequency response of rectangular window.

The frequency response of rectangular window is given by

19. Write the characteristic features of rectangular window.

The characteristic features of rectangular window are

1. The main lobe width is equal to

2. The maximum sidelobe magnitude is -13dB3. The sidelobe magnitude does not decreases significantly with increasing

20. List the features of FIR filter designed using rectangular window.

The features of FIR filter designed using rectangular window are

i) The width of the transition region is related to the width of the mainlobe of window spectrumii) Gibb’s oscillations are noticed in the passband and stop bandiii) The attenuation in the stopband is constant and cannot be varied

21. Write the equation specifying Hanning windows.

The equation for Hanning window is given by

for

= 0 Otherwise.

22. Write the equation specifying Hamming windows.

The equation for Hamming window is given by

for

39

= 0 Otherwise.

23. Write the equation specifying Blackman windows.

The equation for Blackman window is given by

for

= 0 Otherwise.

24. Write the equation specifying Bartlett windows.

The equation for Bartlett window is given by

for

= 0 Otherwise.

25. Write the equation specifying Kaiser windows.

The equation for Kaiser window is given by

for

= 0 Otherwise.Where

is an independent parameter. (x) is the zeroth order Bessel function of the first kind

26. Write the characteristics features of Triangular window.

The characteristic features of Triangular windows are

i) The main lobe width is equal to

ii) The maximum sidelobe magnitude is -25dBiii) The sidelobe magnitude slightly decreases with increasing

40

27. Why the triangular window is not good a good choice for designing FIR filters?

In FIR filters designed using triangular window the transition from passband to stopband is not sharp and the attenuation in stopband is less when compared to filters designed with rectangular window. For the above two reasons the triangular window is not a good choice.

28. List the features of hanning window spectrum.

The features of hanning window spectrum are

i) The mainlobe width is equal to .

ii)The maximum sidelobe magnitude is -31dB.iii)The sidelobe magnitude slightly decreases with increasing .

29. List the features of hamming window spectrum.

The features of hamming window spectrum are

i) The mainlobe width is equal to .

ii)The maximum sidelobe magnitude is -41dB.iii)The sidelobe magnitude remains constant for increasing .

30. Compare the Rectangular and Hanning window.

Sl.No Rectangular window Hanning window1. The width of mainlobe in window

spectrum is

The width of mainlobe in window

spectrum is

2. The maximum sidelobe magnitude in window spectrum is -13dB.

The maximum sidelobe magnitude in window spectrum is -31dB.

3. In window spectrum the sidelobe magnitude slightly decreases with increasing

In window spectrum the sidelobe magnitude decreases with increasing

4. In FIR filter designed using rectangular window the minimum stopband attenuation is 22dB.

In FIR filter designed using Hanning window the minimum stopband attenuation is 44dB.

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31. Compare the Rectangular and Hamming window.

Sl.No Rectangular window Hamming window1. The width of mainlobe in window

spectrum is

The width of mainlobe in window

spectrum is

2. The maximum sidelobe magnitude in window spectrum is -13dB

The maximum sidelobe magnitude in window spectrum is -41dB

3. In window spectrum the sidelobe magnitude slightly decreases with increasing

In window spectrum the sidelobe magnitude remains constant

4. In FIR filter designed using rectangular window the minimum stopband attenuation is 22dB.

In FIR filter designed using Hamming window the minimum stopband attenuation is 51dB

32. Compare the Rectangular and Hamming window.

Sl.No Hanning window Hamming window1. The width of mainlobe in window

spectrum is

The width of mainlobe in window

spectrum is

2. The maximum sidelobe magnitude in window spectrum is -31dB

The maximum sidelobe magnitude in window spectrum is -41dB

3. In window spectrum the sidelobe magnitude decreases with increasing

In window spectrum the sidelobe magnitude remains constant. Here the increased sidelobe attenuation is achieved at the expense of constant attenuation at high frequencies

4. In FIR filter designed using Hanning window the minimum stopband attenuation is 44dB

In FIR filter designed using Hamming window the minimum stopband attenuation is 51dB

33. Compare the Hamming and Blackman window.

Sl.No Hamming window Blackman window1. The width of mainlobe in window

spectrum is

The width of mainlobe in window

spectrum is

42

2. The maximum sidelobe magnitude in window spectrum is -41dB

The maximum sidelobe magnitude in window spectrum is -58dB

3. In window spectrum the sidelobe magnitude remains constant with increasing

In window spectrum the sidelobe magnitude decreases rapidly with increasing

4. In FIR filter designed using Hamming window the minimum stopband attenuation is 51dB

In FIR filter designed using Blackman window the minimum stopband attenuation is 78dB

5. The higher value of sidelobe attenuation is achieved at the expense of constant attenuation at high frequencies

The higher value of sidelobe attenuation is achieved at the expense of increased mainlobe width

34. Write the features of Blackman window spectrum.

The features of Blackman window spectrum are

i) The main lobe width is equal to .

ii) The maximum sidelobe magnitude is -58dBiii) The sidelobe magnitude slightly decreases with increasing iv) The higher value of sidelobe attenuation is achieved at the expense

of increased mainlobe width

35. Write the features of Kaiser Window spectrum.

The features of Kaiser window spectrum are

i) The width of mainlobe and the peak sidelobe are variableii)The parameter in the Kaiser window function , is an independent variable that can be varied to control the sidelobe levels with respect to mainlobe peak iii) The width of the mainlobe in the window spectrum ( and so the transition region in the filter) can be varied by varying the length N of the window sequence

36. Compare the Hamming and Kaiser window.

Sl.No Hamming window Kaiser window1. The width of mainlobe in window

spectrum is

The width of mainlobe in window spectrum depends on the values of and N

2. The maximum sidelobe magnitude The maximum sidelobe magnitude with

43

in window spectrum is -41dB respect to peak of mainlobe is variable using the parameter

3. In window spectrum the sidelobe magnitude remains constant with increasing

In window spectrum the sidelobe magnitude decreases with increasing

4. In FIR filter designed using Hamming window the minimum stopband attenuation is 51dB

In FIR filter designed using Kaiser window the minimum stopband attenuation is variable and depends on the value of

UNIT –V

FINITE WORD LENGTH EFFECTS

1. What are the classification digital signal processors?

The digital signal processors are classified as

i. General purpose digital signal processorsii. Special purpose digital signal processors

2. Write some examples for fixed point DSPs.

TMS320C50, TM 320C54, TM 320C55, ADSP-219x, ADSP-219xx.

3. Write some examples for floating point DSPs.

TMS320C3x, TMS320C67x, ADSP-21xxx.

4. What are the factors that influence selection of DSPs?

The factors that influence selection of DSPs are

1.Architectural features2.Execution speed3.Type of arithmetic4.Word length

5. What are the applications of PDSPs?

44

Digital cell phones, automated inspection, voicemail, motor control, video conferencing, Noise cancellation, Medical imaging, speech synthesis, satellite communication etc.

6. What are the advantages and disadvantages of VLIW architecture?

The advantages of VLIW architecture are

1. Increased performance2. Better compiler targets3. Potentially scalable4. Potentially easier to program5. Can add more execution units, allow more instruction to be

packed into the VLIW instruction.

The disadvantages of VLIW architecture are

1.New kind of programmer/compiler complexity2.Program must keep track of instruction scheduling 3.Increased memory use4.High power consumption5.Misleading MIPS ratings

7. What is pipelining?

Pipelining a processor means breaking down its instruction into a series of discrete pipeline stages which can be completed in sequence by specialized hardware.

8. What is pipeline depth?

The number of pipeline stages is referred to as the pipeline depth.

9. What is the pipeline depth of TMS320C50, TM 320C54x?

TMS320C50 – 4TM 320C54x – 6

10. What are the different stages in pipelining?

The different stages in pipelining are

i. the Fetch phase ii. the Decode phase iii. Memory read phase

45

iv. the Execute phase

11.What are the different buses of TM 320C5x and their functions?

The ‘C5x architecture has four buses

1.Program bus (PB)2.Program address bus (PAB)3.Data read bus (DB)4.Data read address bus (DAB)

The program bus carriers the instruction code and immediate operands from program memory to the CPU.

The program address bus provides address to program memory space for both read and write.

The data read bus interconnects various elements of the CPU to data memory spaces.

The data read address bus provides the address to access the data memory spaces.

12. List the various registers used with ARAU.

The various registers used with ARAU are

1. Eight auxiliary registers (AR0 –AR7)2. Auxiliary register pointer (ARP)

13. What are the elements used for the control processing unit of ‘c5X?

The elements used for the control processing unit of ‘c5X are

1. Central arithmetic logic unit (CALU)2. Parallel logic unit (PLU)3. Auxiliary register arithmetic unit (ARAU)4. Memory mapped registers5. Program controller

46

14. What is the function of parallel logic unit?

The parallel logic unit is second logic units, which execute logic operations on data without affecting the contents of accumulator.

15. List the on chip peripherals in ‘c5x.

The on-chip peripherals interfaces connected to the ‘c5x CPU include

(i) Clock generator(ii) Hardware timer(iii) Software programmable wait state generators(iv) General purpose I/O pins(v) Parallel I/O ports(vi) Serial port interface(vii) Buffered serial port(viii) Time-divisions multiplexed (TDM) serial port(ix) Host port interface(x) User unmaskable interrupts

16. What are the general purpose I/O pins?

Branch control input External flag (XF)

17. What are the arithmetic instructions of ‘C5x?

ADD, ADDB, ADDC, SUB, SUBB, MPY and MPYU.

18. What are the logical instructions of ‘c5x?

AND, ANDB, OR, ORB, XOR and XORB

19. What are the shift instructions?

ROR, ROL, ROLB, RORB and BSAR

20. What are load/store instructions?

LACB, LACC, LACL, LAMM, LAR, SACB, SACH, SACL and SAR

21. What are the different types of arithmetic in digital systems?

47

There are three types of arithmetic used in digital systems are1.Fixed point arithmetic2. Floating point arithmetic3. Block Floating arithmetic

22. What do you understand by a fixed-point number?

In fixed-point arithmetic the positions of the binary point is fixed. The bits to the right represent the fractional part of the number and those to the left represent the integer part. For example, the binary number 01.1100 has the value 1.75 in decimal.

23. What is meant by block floating point representation? What are its advantages?

In block floating point arithmetic the set of signals to be handled is divided into blocks. Each block has the same value for the exponent. The arithmetic operations with in the block uses fixed point arithmetic and only one exponent per block is stored thus saving memory. This representation of numbers is most suitable in certain FFT flow graphs and in digital audio applications.

24. What are the advantages of floating point arithmetic?

The advantages of floating point arithmetic are

1.Larger dynamic range2.Overflow in floating point representation is unlikely.

25. Compare the fixed point and floating point arithmetic

Fixed Point Arithmetic Floating Point Arithmetic1.Fast Operation Slow Operation2.Relatively economical More expensive because of costlier

hardware3.Small dynamic range Increased dynamic range4.Round off error occur only for additions

Round off errors can occur with both additions and multiplication

5.Overflow occur in addition Overflow does not arise6.Used in small computers Used in larger, general purpose

computers

26. What are the three quantization errors due to finite word length registers in digital filters?

48

The three quantization errors due to finite word length registers in digital filters are

1. Input quantization error2. Coefficient quantization error3. Product quantization error

27. How the multiplication and addition are carried out in floating point arithmetic?

In floating point arithmetic, multiplications are carried out as followsLet f1 = M1 x 2c1 and f2 = M2 x 2c2. Then f3 = f1x f2 = (M1xM2)2(c1+c2)

That is, mantissas are multiplied using fixed point arithmetic and the exponents are added.

The sum of two floating point numbers is carried out by shifting the bits of the mantissa of the smaller number to the right until the exponents of the two number are equal and then adding the mantissas.

28. Brief on coefficient inaccuracy. (or)

What is coefficient quantization error? What is its effect?

The filter coefficients are computed to infinite precision in theory. But, in digital computation the filter coefficients are represented in binary and are stored in registers.

If a b bit register is used, the filter coefficients must be rounded or truncated to b bits, which produces an error.

Due to quantization of coefficients, the frequency response of the filter may differ appreciably from the desired response and some times the filter may actually fail to meet the desired response and some times the filter may actually fail to meet the desired specifications. If the poles of desired filter are close to the unit circle, then those of the filter with quantized coefficients may lie just outside the unit circle, leading to unstability

29. What is product quantization error (or) What is product round off error in DSP?

49

Product quantization errors arise at the output of a multiplier. Multiplication of a b bit data with a b bit coefficient results a product having 2b bits. Since a b bit register is used, the multiplier output must be rounded or truncated to b bits, which produces an error. This error is known as product quantization error.

30 What do you understand by input quantization error?

In DSP, the continuous time input signals are converted into digital using a b bit ADC. The representation of continuous signal amplitude by a fixed digit produce an error, which is known as input quantization error.

31. What is truncation?

Truncation is process of reducing the size of binary number by discarding all bits less significant than the least significant bit that is retained. (In the truncation of a binary number to b bits all the less significant bits beyond b th bit are discarded)

32. What is rounding?

Round is the process of reducing the size of a binary number to finite word size of b bits such that, the rounded b-bit number is closest to the original unquantized number.

33. What is Quantization step size?

In digital systems, the numbers are represented in binary. With b-bit binary we can generate 2b different binary codes. Any range of analog value to be represented in binary should be divided into 2b levels with equal increment. The 2b

levels are called Quantization levels and the increment in each level is called Quantization step size . It R is the range of analog signal then,

Quantization step size, q = R/2b.

34. What are limit cycle?

In recursive systems when the input is zero or some nonzero constant value, the nonlinearities due to finite precision arithmetic operations may cause periodic oscillations in the output. These oscillations are called limit cycle.

35. What is zero input limit cycle?

In recursive system, the product Quantization may create periodic oscillations in the output. These oscillations are called limit cycles. If the system

50

output enters a limit cycle, it will continue to remain in limit cycle even when the input is made zero. Hence these limit cycles are also called zero input limit cycles.

36. What is dead band?

In a limit cycle the amplitudes of the output are confined to a range of values, which is called dead band of the filter.

37. How the system output can be brought out of limit cycle?

The system output can be brought out of limit cycle by applying an input of large magnitude, which is sufficient to drive the system out of limit cycle.

38. What is overflow limit cycle?

In fixed point addition the overflow occurs when the sum exceeds the finite word length of the register used to store the sum. The overflow in addition may lead to oscillations in the output which is called overflow limit cycle.

39. How overflow limit cycle can be eliminated?

The overflow limit cycles can be eliminated either by using saturation arithmetic or by scaling the input signal to the adder.

40. What is saturation arithmetic?

In saturation arithmetic when the result of arithmetic operations exceeds the dynamic range of number system, then the result is set to maximum or minimum possible value. If the upper limit is exceeded then the result is set to maximum possible value. If the lower limit is exceeded then the result is set to minimum possible value.

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