DHANALAKSHMI COLLEGE OF ENGINEERING

DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING

QUESTION BANK

DIGITAL SIGNAL PROCESSING

SUBJECT CODE: CS2403 YEAR: III IT/ IV CSE

UNIT – I

SIGNALS AND SYSTEMS

PART A

Z – Transform

1. What is meant by region of convergence? (April/May 2008)

2. What are the properties of z-transform? (Nov/Dec 2008)

3. State Parseval’s relation in z-transform. (April/May 2011)

4. What is the relationship between z-transform and DTFT? (Nov/Dec 2010)

Discrete time signals

1. State the classification of signal. (Nov/Dec 2010)

2. What are energy and power signals? (Nov/Dec 2012)

3. Define – Signal Processing

4. Distinguish between continuous time signal and discrete time signal.

5. Define – Digital Signal

6. What is deterministic signal? State some examples.

7. What is random signal?

8. Define – (a) Periodic Signal (b) Non – Periodic Signal

9. Define – Anti Symmetric Signals

10. What are the types of signal representation?

11. What are the types of operations performed on discrete time signal?

Discrete time systems

1. What is Linear Time – Invariant system? (Nov/Dec 2010)

2. Define – Discrete System

3. State the classification of discrete time system.

4. What is meant by static system?

5. What is meant by causal system?

1

6. Define – Stable System

7. What is meant by linear system?

8. What is unit sample response (impulse response) of a system and state its significance?

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

Sampling Theorem

1. State Sampling theorem. (April/May 2011)

2. Define – Nyquist Rate (Nov/Dec 2008)

3. What is meant by aliasing effect? (April/May 2008)

4. What is an anti-aliasing filter? (Nov/Dec 2008)

5. Define – Resolution or Quantization step size (Nov/Dec 2006)

6. What is the condition for the impulse response to be stable?

7. What is meant by discrete linear convolution?

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

9. What is meant by sampling process?

10. What is meant by quantization process?

11. How can aliasing be avoided?

12. What is meant by critical sampling?

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

14. What is meant by quantization error?

15. What is quantization level?

16. What is SQNR?

17. What is the use of a sample and hold circuit?

18. Define – Conversion Time

19. Define – Resolution in terms of Voltage

20. Define – Resolution in terms of Percentage

21. What are the advantages and disadvantages of counter - ramp type ADCs?

22. What are the advantages and disadvantages of SAADC?

2

UNIT – II

FREQUENCY TRANSFORMATIONS

PART A

Discrete Fourier Transform

1. Define – Fourier Transform of a discrete time signal (April/May 2008)

2. State applications of Fourier transform. (Nov/Dec 2010)

3. Distinguish between Fourier transform of discrete time signal and analog signal.

4. Write the equation for Inverse Fourier Transform.

Properties of DFT

1. State any four properties of DFT. (Nov/Dec 2008)

2. What is zero padding? (May/June 2009)

3. Define – Circular Convolution (May/June 2009)

Filtering methods based on DFT

1. What is the frequency response of an LTI system?

2. What are the properties of an LTI system?

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

4. Write short notes on the frequency response of second order system.

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

6. When is DFT {X(k)} of a sequence x(n) imaginary?

7. When is DFT {X(k)} of a sequence x(n) real?

8. State circular frequency shifting property of DFT.

9. What is meant by convolution?

Fast Fourier Transform

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

FFT? (Nov/Dec 2004)

2. How many multiplications and additions for direct computation of N-point DFT?

(April/May

2008)

3. Calculate the number of multiplications needed in the computation of DFT and FFT with 64-

point sequence. (May/June 2009)

3

4. Distinguish between DIT and DIF algorithms. (May/June 2006)

5. What are the applications of FFT algorithms? (Nov/Dec 2006)

6. What is FFT?

7. What is the speed improvement factor in calculating 64-point DFT of a sequence using direct

computation and FFT algorithms?

8. What is meant by radix-2 FFT?

9. Why is FFT of a discrete time signal called signal spectrum?

4

UNIT – III

IIR FILTER DESIGN

PART A

Infinite Impulse Response

1. Distinguish between FIR and IIR filter. (Nov/Dec 2008)

2. What are the advantages of Direct form- II realization over Direct form –I realization?

(Nov/Dec

2008)

3. What are the types of structures to realize IIR systems?

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

5. 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.

Analog Filter Design

1. Compare Butterworth filter with Chebyshev Type -1 filter. (May/June 2009)

2. What is transposed structure?

3. What is canonic form structure?

4. What are the disadvantages of direct form realizations?

5. What is the advantage of cascade realization?

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

7. What is the general form of IIR filter?

8. Write the no correction magnitude of Butterworth filter. What is the effect of order (N) on

magnitude and phase response?

9. State any two properties of Butterworth low pass filter.

10. What is Butterworth approximation?

11. What is Chebyshev approximation?

12. What is Type-1 Chebyshev approximation?

13. What is Type-2 Chebyshev approximation?

14. Write the magnitude function of Chebyshev low pass filter?

5

15. How does the order of the filter affect the frequency response of Chebyshev filter?

16. How will you determine the order N of Chebyshev filter?

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

18. How are the digital filters designed from the analog filters?

19. Write any two procedures to digitize an analog filter.

Bilinear Transformation

1. What is bilinear transformation? (April/May 2008)

2. What is frequency warping? (Nov/Dec 2008)

3. What is prewarping? What is the use of prewarping? (April/May 2008)

4. What is meant by impulse invariant transformation?

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

6. What is the relation between digital and analog frequency in bilinear transformation?

7. Define – Prewarping in IIR filter

High Pass Filter

1. Define – Signal Flow Graph

2. What are the design techniques for designing HPF filters?

3. What is meant by linear phase response?

Band Pass Filter

1. What are the design techniques for designing BPF filters?

Band Reject Filter

1. What are the design techniques for designing BRF filters?

6

UNIT – IV

FIR FILTER DESGIN

PART A

Finite Impulse Response

1. Write the procedure for designing FIR filter by Fourier series method. (April/May 2008)

2. What are the properties of FIR filter?

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

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

Linear Phase FIR Filter

1. What is the necessary condition for the linear phase characteristic of a FIR filter?

(May/June

2006)

2. State the design techniques for linear phase FIR filter. (May/June 2006)

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

Windowing Technique

1. What are the desirable characteristics of the window? (May/June 2009)

2. Write the equation for Hanning window function. (Nov/Dec 2010)

3. Write the equation for Hamming window function. (Nov/Dec 2004)

4. Write the equation for Blackman window function. (Nov/Dec 2010)

5. Write the equation for Bartlett window function. (Nov/Dec 2004)

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

7. Write the characteristic features of rectangular window.

8. State the features of FIR filter designed using rectangular window.

9. Write the equation for Kaiser Windows.

10. Write the characteristic features of Triangular window.

11. State the features of Hanning window spectrum.

12. State the features of hamming window spectrum.

13. Compare the Rectangular with Hanning window.

14. Compare the Hamming with Blackman window.

7

15. State the features of Blackman window spectrum.

16. State the features of Kaiser window spectrum.

Frequency Sampling Technique

1. What is Gibbs phenomenon? (Nov/Dec 2004)

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

UNIT –V

APPLICATIONS

PART A

Multi rate signal processing

1. Differentiate fixed point arithmetic from floating point arithmetic. (Nov/Dec 2006)

2. What is product quantization error? (Nov/Dec 2010)

3. What is truncation? (Nov/Dec 2006)

4. What is the need for multi rate signal processing? (Nov/Dec 2012)

5. Distinguish between down sampling and up sampling.

6. Distinguish between decimator and interpolator

Speech processing

1. What is short time Fourier analysis?

2. What is linear prediction analysis?

3. What is channel vocoder?

Musical processing

1. What is the need for musical processing?

Image enhancement

1. State any two image enhancement methods. (April/May 2011)

2. What is anti imaging filter

Adaptive Filter

1. What is adaptive equalization? (Nov/Dec 2012)

8

UNIT-I

SIGNALS AND SYSTEMS

PART B

Z – Transform

1. Find inverse Z – transform of

X(Z) = if

a) ROC: |Z| > 1, b) ROC: |Z| < 0.5, c) ROC: 0.5 < |Z| <1. (12) (Nov/Dec 2010)

2. Determine the transfer function, and impulse response of the system

y(n) – y(n – 1) + y(n – 2) = x(n) + x(n – 1). (8) (May/June 2009)

3. Find the Z-transform of

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

Compute the system function H(Z) and the unit sample response of the system in analytical

form. (8) (May/June 2009)

4. Consider a system y(n) + y(n – 1) = x(n) + x(n – 1). Find transfer function, and impulse

response the system. (8)

5. Derive expressions to relate Z-transform and DFT. (8)

6. State and explain the scaling and time delay properties of Z transform. (8)

Discrete time signals

1. Find the convolution of the signals x(n) = and h(n) = u(n). (8)

2. Explain the classification of signals with examples. (8)

Discrete time systems

1. Explain any four properties of LTI system with examples for each.

(16) (Nov/Dec 2008)

2. Explain the classification of systems with examples. (8)

9

Convolution

1. Find the convolution sum of

and h(n) = δ(n) – δ(n – 1) + δ(n – 2) – δ(n – 3). (8) (May/June 2009)

2. Distinguish between linear and circular convolution with examples. (16)

UNIT – II

FREQUENCY TRANSFORMATIONS

PART B

Discrete Fourier Transform

1. Using DFT and IDFT method, perform circular convolution of the sequences

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

h(n) = {1, 2, 3}. (10)(April/May 2011)

2. Compute the 8 point DFT of the sequence x(n) = [1, 2, 3, 4, 4, 3, 2, 1] using radix-2 DIT and DIF

algorithms. (16)(May/June 2009)

3. Compute the 8 point DFT of the sequence x(n) = [1,2,3,4,4,3,2,1]. (10)(April/May 2008)

4. Compute DFT of the following sequences (8)

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

(2) x(n) = {j, 0, j, 1}

5. Find DFT of the sequence x(n) = { 1, 1, 1, 1, 1, 1, 0, 0} using radix-2 DIF FFT algorithm. (16)

6. Compute the eight point DFT of the given sequence x(n) = { ½, ½, ½, ½, 0, 0, 0, 0} using radix-2

DIT DFT algorithm. (16)

Properties of DFT

1. State the properties of DFT. (8)(May/June 2009)

2. Illustrate the circular convolution property of DFT. (10)(April/May 2008)

Filtering methods based on DFT

1. Explain in detail the decimation in time algorithm with suitable examples. (16)

2. Explain in detail the decimation in frequency algorithm with suitable examples. (16)

10

Fast Fourier Transform

1. Derive and draw the flow graph of the radix-2 DIF FFT algorithm for the computation of 8-point

DFT. (10)(April/May 2008)

UNIT – III

IIR FILTER DESIGN

PART B

Infinite Impulse Response

1. Explain in detail the concepts of impulse invariance method of IIR filter design and

summarize the design steps. (16)(May/June 2009)

2. Obtain the cascade and parallel form realization structures for the system given by the difference

equation y ( ) = – 0 .1 ( – 1) + 0.2 ( – 2) + 3 ( ) + 3.6 (n-1)+0.6 ( – 2).

(8)(Apr/May

2008)

3. Design IIR filter using impulse invariance technique. Given that and

implement the resulting digital filter by adder, multipliers and delays. Assume sampling

period =1 sec. (8)

4. Obtain the direct form I, canonic form and parallel form realization structures for the system

given by the difference equation

y( ) = – 0 .1 ( – 1) + 0.72 ( – 2) + 0.7 ( ) – 0.252 ( – 2). (8)

5. If , find using impulse invariant method for sampling frequency of

5 samples/sec. (8)

Analog Filter Design

11

1. Design Butterworth filter using bilinear transformation method for the following

specifications

0.8 ≤ |H(ejω)| ≤ 1; 0 ≤ ω ≤ 0.2π

|H(ejω)| ≤ 0.2; 0.6 ≤ ω ≤ π

(16)(Nov/Dec 2012)

2. Find H(s) for the third order low pass Butterworth filter.

(6)(April/May 2008)

3. Design digital low pass filter using bilinear transformation. Given that

Assume sampling frequency of 100 rad/ sec. (8)

4. Explain the round off effect in digital filters. (10)

5. Explain in detail the designing methods of IIR filters from analog filters. (16)

6. Compare FIR with IIR filters. (8)

Bilinear Transformation

1. Design a digital filter with H(s) = 1/(s2+7s+12) using T = 1sec. (8)(April/May 2008)

2. Design digital low pass filter using BLT for H(s) = 2/{(S+1)(S+2)} with cut-off frequency

of 100 rad/sec and sampling time T = 1.2ms. (8)(April/May 2008)

3. Design an IIR digital low pass Butterworth filter to meet the following requirements: Pass

band ripple (peak to peak) ≤ 0.5dB, Pass band edge: 1.2kHz, Stop band attenuation ≥ 40dB,

Stop band edge: 2.0 kHz, Sampling rate: 8.0 kHz. Use bilinear transformation technique. (16)

12

UNIT – IV

FIR FILTER DESGIN

PART B

Finite Impulse Response

1. Design a symmetric FIR low pass filter whose desired frequency response is given as

( ) =

The length of the filter should be 7 and = 1 rad/sample using rectangular window.

(16)

(May/June 2009)

2. Determine the first 15 coefficients of FIR filters with magnitude specification given below using

frequency sampling method:

( ) = (12)

3. Explain the effect of finite word length on digital filter. (10)

Linear Phase FIR Filter

1. For an FIR linear phase digital filter approximating the ideal frequency response,

13

( ) =

Determine the coefficients of a 5 tap filter using rectangular window.

(10)(April/May 2008)

2. Determine the coefficients h(n) of a linear phase FIR filter of length M = 15 which has a

symmetric unit sample response and a frequency response

Hr =

(12)(May/June 2009)

3. Determine the unit sample response ( ) of a linear phase FIR filter of length M = 4 for which

the frequency response at and is given as r(0) = 1 and Hr(

(8)

Windowing Technique

1. Explain any three window techniques used in the design of FIR filters. (16)(April/May 2008)

Frequency Sampling Technique

1. State the advantage of floating point representation over fixed point representation. (8)

2. Explain in detail the type-I frequency sampling method of designing an FIR filter. (8)

14

UNIT –V

APPLICATIONS

PART B

Multi rate signal processing

1. Derive and explain in detail the frequency domain characteristics of the decimator by the

factor M and interpolator by the factor L. (12)(April/May 2011)

2. With neat diagram and supportive derivation explain in detail multirate signal processing

using two techniques. (16)

3. Explain in detail decimation of sampling rate by an integer factor D and derive spectra for

decimated signal. (16)

15

Speech processing

1. Write short notes on

a) Speech Processing

b) Vocoder (8)

Musical processing

1. Write notes on:

a) Sub band coding of speech signals.

(8)

b) Musical sound processing.

(8)

Adaptive Filter

1. With neat diagram explain in detail any two applications of adaptive filter using LMS

algorithm. (12)(April/May 2011)

2. Explain in detail : (Nov/Dec 2012)

a) Adaptive noise cancellation with a neat block diagram (8)

b) Image enhancement techniques (8)

3. What is adaptive filter? With neat block diagram explain any four applications of adaptive

filter. (16)

4. Discuss in detail various quantization effects in the design of digital filters. (12)

16