Anna University, Chennai

**M**

**.**

**A**

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**M SCHOOL OF ENGINEERING, SIRUGANUR, DEPARTMENT OF ELECTRONICS**

**&****C****O****MM****UN****ICATIONENGINEERING**

__QUESTION BANK__

**S****UBJECT CODE/NAME: EC1307 DIGITAL SIGNAL PROCESSING**

**YEAR / SEM : III / V**

__UNIT – I__** SIGNALS**

__P____A____R____T – A (2 MARKS)__

1. Define Signal.

2. Define a system.

3. What are the steps involved in digital signal processing?

4. Give some applications of DSP?

5. Write the classifications of DT Signals.

6. What is an Energy and Power signal?

7. What is Discrete Time Systems?

8. Write the Various classifications of Discrete-Time systems.

9. Define linear system

10. Define Static & Dynamic systems

11. Define causal system.

12. Define Shift-Invariant system.

13. Define impulse and unit step signal.

14. What are FIR and IIR systems?

15. What are the basic elements used to construct the block diagram of discrete time system?

16. Define sampling theorem.

17. Check the linearity and stability of g(n),

18. What are the properties of convolution?

19. Give the classification of signals?

20. What are the types of systems?

21. What are even and odd signals?

22. What are the elementary signals and name them?

23. What are the properties of a system?

24. What is an invertible system?

25. Define unit step, ramp and delta functions for

CT.

26. Define random signals.

27. Define Aliasing.

28. Define Nyquist rate.

29. What are the used to avoid aliasing?

30. Define Sampling theorem.

31. What is Nyquist interval?

32. Define symmetric and Anti symmetric signals. How do you prevent aliasing while sampling a CT

signal?

33. What is SISO system and MIMO system?

34. Define Quantization.

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35. Write down the exponential form of the Fourier series representation of a Periodic signal?

36. Write down the trigonometric form of the Fourier

series representation of a periodic signal?

37. Write short notes on dirichlets conditions for

Fourier series.

38. State Time Shifting property in relation to

Fourier series.

__P____A____R____T – B__

1. Explain in detail about the classification of discrete time systems. (16)

2. (a) Describe the different types of discrete time signal representation. (6)

(b) Define energy and power signals. Determine

whether a discrete time unit step signal x(n) =

u(n) is an energy signal or a power signal. (10)

3. (a) Give the various representation of the given discrete time signal

x(n) = {-1,2,1,-2,3} in Graphical, Tabular, Sequence, Functional and Shifted functional. (10)

(b) Give the classification of signals and explain it. (6)

4. (a) Draw and explain the following sequences:

i) Unit sample sequence ii) Unit step sequence iii) Unit ramp sequence

iv) Sinusoidal sequence and v) Real exponential sequence (10)

(b) Determine if the system described by the following equations are causal or noncausal i) y(n) = x(n) + (1 / (x(n-1)) ii) y(n) = x(n2) (6)

5. Determine the values of power and energy of the

following signals. Find whether the signals are power, energy or neither energy nor power signals.

i) x(n) = (1/3)n u(n) ii) x(n) = ej((π/2)n +

(π/4)

iii) x(n) = sin (π/4)n iv) x(n) = e2n u(n) (16)

6. (a) Determine if the following systems are time- invariant or time-variant

i) y(n) = x(n) + x(n-1) ii) y(n) = x(-n) (4)

(b) Determine if the system described by the following input-output equations are linear or non- linear.

i) y(n) = x(n) + (1 / (x(n-1)) ii) y(n) =

x2(n) iii) y(n) = nx(n) (12)

7. Test if the following systems are stable or not. i) y(n) = cos x(n) ii) y(n) = ax(n)

iii) y(n) = x(n) en iv) y(n) = ax(n)

(16)

8. (a) Determine the stability of the system

2

y(n) – (5/2)y(n-1) + y(n-2) = x(n) – x(n1) (8)

(b) Briefly explain about quantization. (8)

9. (a) Explain the principle of operation of analog to digital conversion with a neat diagram. (8)

(b) Explain the significance of Nyquist rate and aliasing during the sampling of continuous time

signals. (8)

10. (a) List the merits and demerits of Digital signal processing. (8)

(b) Write short notes about the applications of

DSP.

11. A discrete time system can be static or dynamic, linear or non-linear, Time variant or time invariant, causal or non causal, stable or unstable. Examine the following system with respect to the properties also.

(i) y(n) = log10[{x(n)}] (ii) y(n) = x(-n-2)

(iii) y(n) = cosh[nx(n) + x(n-1)]

13. Compute the convolution of the following signals x(n) = {1,0,2,5,4} h(n) = {1,-1,1,-1}

↑ ↑

h(n) = {1,0,1} x(n) = {1,-2,-2,3,4}

↑ ↑

14. Find the convolution of the two signals x(n) = 3nu(-n); h(n) = (1/3)n u(n-2) x(n) = (1/3) –n u(-n-1); h(n) = u(n-1)

x(n) = u(n) –u(n-5); h(n) = 2[u(n) – u(n-3)]

15. a) Determine the impulse response of the filter defined by y(n)=x(n)+by(n1)

b) A system has unit sample response h(n) given

by

1) y(n)=cos(x(n))

2) y(n)=x(-n+2)

3) y(n)=x(2n)

4)y(n)=x(n) cos ωn

12. a) i) Determine the response of the causal system y(n)-y(n-1)=x(n)+x(n-1) to inputs x(n)=u(n) and x(n)=2 –n u(n).Test its stability

b) Determine whether each of the following systems defined below is (i) casual (ii) linear (iii) dynamic (iv) time invariant (v) stable

h (n)=-1/δ(n+1)+1/2δ(n)-1-1/4 δ(n-1). Is the system BIBO stable? Is the filter causal? Justify your answer.

16. Check whether the following systems are linear

or not.

a) y(n)=x 2 (n) b) y(n)=n x(n)

17. For each impulse response listed below, determine if the corresponding system is i) causal ii)

stable

1) 2 n u(-n)

2) sin nЛ/2

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3) δ(n)+sin nЛ

4) e 2n u(n-1)

18. Explain with suitable block diagram in detail about the analog to digital

conversion and to reconstruct the analog signal

19. Find the cross correlation of two sequences x(n)={1,2,1,1} y(n)={1,1,2,1}

20. Determine whether the following systems are linear, time invariant

1) y(n)=A x(n)+B

2) y(n)=x(2n)

__UNIT – II__

**DISCRETE TIME SYSTEM ANALYSIS PART – A (2 MARKS)**

1. Define Z-transform.

2. What is meant by Region of convergence?

3. What are the properties of ROC?

4. List the properties of z-transform.

5. Explain the linear property of z-transform.

6. Explain the time-shifting property of z-transform.

7. What are the different methods of evaluating inverse z-transform?

8. What are the properties of frequency response

H(eiω) of an LTI system?

9. What is the necessary and sufficient condition on the impulse response of stability?

10. Distinguish between Linear convolution and

circular convolution.

11. How will you obtain linear convolution from circular convolution?

12. What is meant by sectioned convolution?

13. What are the two methods used for the sectional convolution?

14. Distinguish between Overlap add and Overlap save method.

15. Distinguish between DFT and DTFT.

16. Distinguish between Fourier series and Fourier transform.

17. Define DTFT.

18. List the properties of DTFT.

19. Define DFT.

20. Define circularly even sequence.

21. Define circularly odd sequence.

22. State circular convolution.

23. State parseval’s theorem.

24. Find Z transform of x(n)={1,2,3,4}

25. State the convolution property of Z transform.

26. State initial value theorem.

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__P____A____R____T – B__

1. (a) Obtain the transfer function and impulse response of the LTI system defined by y(n-2)+5y(n-

1)+6y(n)+x(n) (8)

(b) State and prove convolution property of discrete time Fourier transform. (8)

2. (a) State and prove any tow properties of z- transform. (8)

(b) Find the z-transform and ROC of the causal sequence. (4)

X(n) = {1,0,3,-1,2}

(c) Find the z-transform and ROC of the anticausal sequence (4)

X(n) = {-3,-2,-1,0,1}

3. (a) Determine the z-transform and ROC of the signal

i) x(n) = anu(n) and

ii) x(n) = -bnu(-n-1) (12)

(b) Find the stability of the system whose impulse

response h(n) = (2)nu(n) (4)

4. (a) Determine the z-transform of x(n) = cos ωn

u(n) (6)

(b) State and prove the following properties of z- transform. (10)

i) Time shifting ii) Time reversal iii) Differentiation

iv) Scaling in z-domain

. (a) Determine the inverse z-transform of x(z) = (1+3z-1) / (1+3z-1+2z-2) for z >2 .(8)

(b) Compute the response of the system

y(n) = 0.7y(n-1)-0.12y(n-2)+x(n-1)+x(n-2) to input x(n) = nu(n).Is the system is stable (8)

6. Find the inverse z-transform of x(z) = (z2+z) / (z-

1)(z-3), ROC: z > 3. Using (i) Partial fraction method, (ii) Residue method and (iii) Convolution method. (16)

7. (a) Determine the unit step response of the system

whose difference equation is y(n)-0.7y(n-1)+0.12y(n-

2) = x(n-1)+x(n-2) if y(-1) = y(-2) = 1. (8)

(b) Find the input x(n) of the system, if the impulse response h(n) and the output y(n) as shown below.

(8)

h(n) = {1,2,3,2} y(n) = {1,3,7,10,10,7,2}

8. (a) Determine the convolution sum of two sequences x(n) = {3,2,1,2}, h(n) = {1,2,1,2} (8)

(b) Find the convolution of the signals

x(n) = 1 n = -2,0,1

= 2 n = -1

= 0 elsewhere

h(n) = δ(n)-δ(n-1)+ δ(n-2)- δ(n-3) (8)

9. (a) Determine the output response y(n) if h(n) =

{1,1,1,1}; x(n) = {1,2,3,1} by using i) Linear

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convolution ii) Circular convolution and iii) Circular convolution with zero padding. (12)

(b) Explain any twp properties of Discrete Fourier

Transform. (4)

10. Using linear convolution find y(n) = x(n)*h(n) for the sequences x(n) = (1,2,-1,2,3,-2, -3,-1,1,1,2,-1) and h(n) = (1,2).Compare the result by solving the

problem using i) Over-lap save method and ii) Overlap – add method. (16)

11. For the sequences given below, find the frequency response, plot magnitude response, phase

response and comment. (16)

i) x(n) = 1 for n = -2,-1,0,1,2

= 0 otherwise

ii) x(n) = 1 for n = 0,1,2,3,4

= 0 otherwise

12. (a) Calculate the frequency response for the LTI

systems representation

i) h(n) = [1/n]n u(n) ii) h(n) = δ(n) – δ(n-

1) (8)

(b) Find the frequency response of the system having impulse response

h(n) = [1/2] { (1/2)n + (-1/4)n } u(n) (8)

13. Determine the frequency response (H(ejω)) for the system and plot magnitude response and phase response. y(n)+[1/4]y(n-1) = x(n)-x(n-1) (16)

14. (a) A discrete – time system has a unit sample response h(n) given by

h(n) = [1/2] δ(n) + δ(n-1) + [1/2] δ(n-2). Find the system frequency response H(ejω); Plot magnitude and Phase response. (12)

(b) Explain any two properties of Discrete Fourier

Series. (4)

__UNIT – III__

**DISCRETE FOURIER TRANSFORM AND COMPUTATION**

__P____A____R____T – A (2 MARKS)__

1. Why FFT is needed?

2. What is the main advantage of FFT?

3. What is FFT?

4, what is meant by Radix-2 FFT?

5. What is decimation-in-time algorithm?

6. What is decimation in frequency algorithm?

7. What are the differences and similarities between

DIF and DIT algorithm?

8. What is the basic operation of DIT algorithm?

9. What is the basic operation of DIF algorithm?

10. What are the applications of FFT algorithms?

11. Draw the flow graph of a two point DFT for a decimation-in-time decomposition.

12. Draw the flow graph of a two point radix-2 DIF FFT.

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13. Draw the basic butterfly diagram for DIT

algorithm.

14. Draw the basic butterfly diagram for DIF

algorithm.

15. Define DFT of a discrete time sequence.

16. What are the differences and similarities between

DIF and DIT algorithms?

17. Define the properties of convolution.

18. Draw the basic butterfly diagram of radix-2 FFT.

19. State and prove parseval’s relation for DFT.

20. What do you mean by the term “bit reversal” as

applied to FFT

21. What are the advantages of FFT algorithm over direct computation of DFT?

22. The first five DFT coefficients of a sequence x(n)

are x(0) = 20, x(1) = 5+j2, x(2) = 0, x(3)=0.2+j0.4, X(4) = 0. Determine the remaining DFT coefficients.

23. Define Complex Conjugate of DFT property.

24. How many multiplications and additions are

required to compute N-point DFT using radix-2

FFT?

25. What are the applications of FFT algorithms?

26. What are twiddle factors of the DFT?

27. How many additions and multiplications are needed to compute N-point FFT?

28. Calculate the number of multiplications in 64 point DFT using FFT?

29. Find the values of WN, when N=8 and k=2 and also for k=3.

30. What are the differences and similarities between

DIF and DIT algorithms?

__P____A____R____T – B__

1. Describe the decimation in time [DIT] radix-2

FFT algorithm to determine N-point DFT. (16)

2. An 8-point discrete time sequence is given by x(n)

= {2,2,2,2,1,1,1,1}. Compute the 8-point DFT of x(n)

using radix-2 FFT algorithm. (16)

3. (a) Compute the 4-point DFT and FFT-DIT for the

sequence x(n) = {1,1,1,3} and What are the basic steps for 8-point FFT-DIT algorithm computation? (12)

(b) What is the advantage of radix-2 FFT algorithm

in comparison with the classical DFT method? (4)

4. (a) Perform circular convolution of the two sequences graphically x1(n) = {2,1,2,1} and x2(n) =

{1,2,3,4} (6)

(b) Find the DFT of a sequence by x(n) =

{1,2,3,4,4,3,21} using DIT algorithm. (10)

5. (a) Explain the decimation in frequency radix-2

FFT algorithm for evaluating N-point DFT of the

7

given sequence. Draw the signal flow graph for N=8. (12)

(b) Find the IDFT of y(k = {1,0,1,0} (4)

6. (a) Find the circular convolution of the sequences x1(n)= {1,2,3} and x2(n) = {4,3,6,1} (8)

(b) Write the properties of DFT and explain. (8)

7. (a) Draw the 8-point flow diagram of radix-2 DIF-

FFT algorithm. (8)

(b) Find the DFT of the sequence x(n) = {2,3,4,5}

using the above algorithm. (8)

8. (a) What are the differences and similarities between DIT and DIF FFT algorithms?(6)

(b) Compute the 8-point IDFT of the sequence

x(k) = {7, -0.707-j0.707, -j,0.707-j0.707, 1,

0.707+j0.707, j, -0.707+j0.707} using DIT

algorithm. (10)

9. (a) Compute the 8-point DFT of the sequence x(n)

= {0.5,0.5,0.5,0.5,0,0,0,0} using radix-2 DIT

algorithm. (8)

(b) Find the IDFT of the sequence

x(k) = {4,1-j2.414,0,1- j0.414,0,1+j.414,0,1+j2.414}

using DIF algorithm. (8)

10. Compute the 8-point DFT of the sequence

x(n) = 1, 0 ≤ n ≤ 7

0, otherwise by using DIT,DIF

algorithms. (16)

11. Find 4-point DFT of the following sequences

(a) x(n)={1,-1,0,0}

(b) x(n)={1,1,-2,-2} (AU DEC 06) (c) x(n)=2n

(d) x(n)=sin(nΠ/2)

12. Find 8-point DFT of the following sequences

(a) x(n)={1,1,1,1,0,0,0,0}

(b) x(n)={1,2,1,2}

13. Determine IDFT of the following (a)X(k)={1,1-j2,-1,1+j2} (b)X(k)={1,0,1,0} (c)X(k)={1,-2-j,0,-2+j}

__UNIT – IV__

__DESIGN OF DIGITAL FILTERS__** **__P____A____R____T – A (2 MARKS)__

1. What is FIR Filter?

2. Write the procedure for designing FIR filters

3. Write the characteristics of FIR filter.

4. What are the design techniques available for the designing FIR filter?

5. What are the demerits of FIR filter?

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

7. What is GIBBS phenomenon?

8. Write the desirable characteristics of frequency response of window functions.

9. Write the characteristics features of rectangular window.

10. List merits and demerits of rectangular window.

11. List the features of Kaiser Window.

12. What do you understand by linear phase response?

13. What are the two types of filter based on the

impulse response?

14. What are the advantages of Kaiser Window?

15. What is the principle of designing FIR filter using frequency sampling method?

16. What are the properties of FIR filter?

17. What is the need for employing window technique for FIR filter design? (Or) What is window and why it is necessary?

18. What is the necessary and sufficient condition for linear phase characteristic in FIRfilter?

19. Define IIR filter.

20. What are the methods available for designing analog IIR filter?

21. What are the methods available for designing analog IIR filter?

22. Mention the importance of IIR filter:

23. Mention the two properties of Butterworth low pass filter.

24. Write the properties of chebyshev type-I filter:

25. What is aliasing? Why it is absent in bilinear transformation ?

26. How one can design digital filter from analog

filter ?

27. What is bilinear transformation?

28. What is warping effect?

29. Write merits and demerits of bilinear

transformation.

30. What is the main advantage of direct-form II realization when compared to directform I realization?

31. What is the main disadvantage of direct-form realization?

32. What is the advantage of cascade realization?

33. Distinguish IIR and FIR.

34. Compare analog and digital filter.

35. Compare Butterworth and Chebyshev Filter:

36. Compare impulse invariant and bilinear technique

37. What are the different types of structures for

realization of IIR systems?

38. Write a short note on prewarping.

__P____A____R____T – B__

1. Describe the impulse invariance and bilinear transformation methods used for designing digital IIR filters. (16)

9

2. (a) Obtain the cascade and parallel realization of the system described by

y(n) = -0.1y(n-1)+0.2y(n-2)+3x(n)+3.6x(n-

1)+0.6x(n-2) (10)

(b) Discuss about any three window functions used in the design of FIR filters. (6)

3. Determine the direct form II and parallel form

realization for the following system.

y(n) = -0.1y(n-1)+0.72y(n-2)+0.7x(n)-

0.252x(n-2) (16)

4. An analog filter has a transfer function H(s) = (10 /

s2+7s+10). Design a digital filter

equivalent to this impulse invariant method. (16)

5. For the given specifications design an analog

Butterworth filter,

0.9 ≤ H(jΩ) ≤ 1 for 0 ≤ Ω ≤ 0.2π

H(jΩ) ≤ 0.2 for 0.4π ≤ Ω π (16)

6. Design a digital Butterworth filter satisfying the constraints

0.707 ≤ H(ejω) ≤ 1 for 0 ≤ ω ≤ π/2

H(ejω) ≤ 0.2 for 3π ≤ ω ≤ π

With T = 1 sec using Bilinear transformation. (16)

7. Design a chebyshev filter for the following specification using impulse invariance method. 0.8 ≤

H(ejω) ≤ 1 for 0 ≤ ω ≤ 0.2π

H(ejω) ≤ 0.2 for 0.6π ≤ ω ≤

8. (a) Write the expressions for the Hamming, Hanning, Bartlett and Kaiser windows.(6)

(b) Explain the design of FIR filters using windows.

(10)

9. Design an ideal high pass filter with

Hd(ejω) = 1 for π/4 ≤ ω ≤ π

= 0 for ω ≤ π/4

Using Hanning window for N=11. (16)

10. Design an ideal high pass filter with

Hd(ejω) = 1 for π/4 ≤ ω ≤ π

= 0 for ω ≤ π/4

Using Hamming window for N=11. (16)

11. Using a rectangular window technique design a lowpass filter with pass band gain of unity, cutoff frequency of 1000 Hz and working at a sampling frequency of 5kHZ. The length of the impulse response should be 7. (16)

12. Design an ideal Hilbert transformer having frequency response

H(ejω) = j for -π ≤ ω ≤ 0

= -j for 0 ≤ ω ≤ π

Using blackman window for N=11.Plot the frequency response. (16)

π (16)

10

__UNIT – V__** **__P____ROGRAMMABLE ____DSP CHIPS__** **__P____A____R____T – A (2 MARKS)__

1. What are the classifications of digital signal processors?

2. What are the factors that influence the selection of

DSPs?

3. What are the applications of PDSPs?

4. Mention the different addressing modes in

TMS320C54x processor.

5. What is meant by pipelining?

6. Give the digital signal processing application with the TMS 320 family.

7. What are the desirable features of DSP Processors?

8. What are the different types of DSP Architecture?

9. State the features of TMS3205C5x series of DSP

processors.

10. Define Parallel logic unit?

11. Define scaling shifter?

12. Define ARAU in TMS320C5X processor?

13. What are the Interrupts available in TMS320C5X

processors?

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

15. What do you understand by input quantization error?

16. What is co-efficient quantization error?

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

18. What are the different methods of quantization?

19. Define Truncation and Rounding.

20. What is the effect of quantization on pole locations?

21. Which realization is less sensitive to the process of quantization?

22. What is meant by quantization step size?

23. What are the two kinds of limit cycle behavior in

DSP?

24. Define “Dead band” of the filter.

25. Explain briefly the need for scaling in the digital filter implementation.

26. Why rounding is preferred to truncation in realizing digital filter?

__P____A____R____T – B__

1. Describe in detail the architectural aspects of TMS320C54 digital signal processor using an illustrative block diagram. (16)

2. Explain the various addressing modes and salient

features of TMS320C54X. (16)

3. (a) Describe the function of on-chip peripherals of

TMS320C54 processor. (12)

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(b) What are the different buses of TMS320C54 and their functions? (4)

4. Describe the errors introduced by quantization.

Explain the impact of quantization of filter coefficients on the location of poles. (16)

5. Write a brief note on:

i) Input quantization (8)

ii) Limit cycles (8)

6. Discuss in detail the various quantization effects in the design of digital filters. (16)

7. Find the effect of co-efficient quantization on pole

locations of the given second order IIR system, when it is realized in direct form I and in cascade form. Assume a word length of 4 bits through truncation. (16)

H(z) = 1 / (1 – 0.9 z-1 + 0.2 z-1)

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