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Digital Signals and Systems

Sample questions

(60% Theory and 40% Problems)

Unit I:

1. What is signal processing?

2. What are the advantages of Digital Signal Processing (DSP) over Analog Signal Processing (ASP)?

3. What are the disadvantages of DSP over ASP?

4. Discuss the applications of DSP.

5. Define & give the graphical representation of the following functions:

i. Unit rampii. Unit step

iii. Unit impulse6. Discuss the classification of Signals.7. Show that the product of two even signals or two odd signals is an even signal and that the product

of an even and an odd signal is an odd signal.

8. With illustrations, explain the following for discretetime signals.

i. Shiftingii. Foldingiii. Time scaling

9. Discuss the classification of systems.

10. Draw and explain the block diagram of an analogtodigital converter.

11. What is meant by sampling? State sampling theorem.

12. What is meant by quantisation and encoding?13. Write down the trigonometric form of the Fourier series representation of a periodic signal.

14. Write a note on Dirichlets conditions.

15. State and prove Parsevals theorem for Fourier transform.

16. Explain the following properties of Fourier Transform

i. Linearityii. Symmetryiii. Scaling

17. Find the Fourier transform of Unit Step Function.

18. Determine the Fourier transform of Signum function & also plot the amplitude and phase spectra.

19. Obtain exponential Fourier series for the following waveform,

20 Simple Problems to be solved for finding

i. Whether given signal is periodic or notii. Whether given signal is energy or power signal etc

Unit II:

1. State and explain Laplace Transform and its inverse transform.

2. What is region of convergence?

3. Find the Laplace transform of

i. Unit step functionii. Sine functioniii. Cosine functioniv. f(t) = t3 + 3t26t + 4

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v. Rectangular pulsevi. Sawtooth pulse

4. Discuss initial value and final value theorems in Laplace transform domain.

5. Find Laplace transform of the periodic rectangular wave form with period 2T

6. Find Laplace transform of the periodic sawtooth waveform with period of one cycle T

7. State any five properties of Laplace transform.

8. Obtain Laplace transform for step and Impulse Responses of

i. Series R-L Circuitii. Series R-C Circuit

9. Define the network transfer function & explain how to obtain output impulse & step response

using transfer function.

10. Determine poles, zeroes of F(s) & plot them graphically. Also obtain f(t) if F(s)=

Simple Problems to be solved

Unit III:

1. Define z-Transform.2. Explain the use of z-Transform.

3. How is z-Transform obtained from Laplace transform?

4. State and explain the properties of z-Transform.

5. Compare the properties of tw-sided z-transform with those of one-sided z-Transform

6. What is the condition for z-Transform to exist?

7. With reference to z-Transform, state and the initial and final value theorem.

8. Obtain the Z-Transformation of x(n)=2nu(n-2).

9. Determine the Z-Transform and the region of convergence of

x(n) =

10 Obtain the Z-Transform of x(n)=n u(n).11. State the Contour-Integration Residue method to calculate Inverse Z-Transformation. Hence

obtain Inverse Z-Transform of X(z) =

.12. Obtain the Z-Transform of the sequence x(n)= {1,2,5,4,6}

Simple Problems to be solved

Unit IV:

1. When a system is said to be linear?

2. Define the termsi. Linearityii. Time invarianceiii. Causality

With reference to discrete time system

3. Simple problems to check the Linearity and Causality of the signals.

4. Explain briefly the Paley-Wiener criterion

5. Explain stability in Linear Time Invariant system. What is the condiction for a system to be BIBO

stable?

6. Check whether the following digital systems are BIBO stable

i. y(n) = ax2(n)ii. y(n) = ax(n) + b7. What is convolution? What are the properties of convolution?

8. What is frequency response? What are the properties of frequency response?

9. Simple examples for frequency response

For example

The output y(n) for an Linear Time Invariant system to the input x(n) is

y(n) = x(n)2x(n-1) + x(n-2)

Compute the magnitude and phase of the frequency response of the system for 10 Check whether the system F[x(n)]= n[x(n)] is Linear and Time-Variant.

11. Obtain Frequency Response for y(n) =x(n)+10y(n-1) with initial condition y(-1)=0.

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Unit V:

1. State and explain the properties of Discrete Fourier Series.

2. Define Discrete Fourier Transform (DFT) for a sequence x(n)

3. Explain any 5 properties of DFT

4. State the relationship between DFT and z-Transform

5.

Determine DFT of the sequence x(n) =

6. Define Discrete Time Fourier Transform (DTFT) and Inverse Discrete Time Fourier Transform

(IDTFT).Explain the difference between Discrete Fourier Transform (DFT) and Discrete Time

Fourier Transform (DTFT).

7. Determine the Circular Correlation values of the two sequences x(n)={1,0,0,1} and

h(n)={4,3,2,1}.

8. What are the methods used to perform Fast Convolution. Explain any one method giving all the

steps involved to perform Fast Convolution.

9. Compute Linear and Circular Periodic Convolutions of the sequence x1(n)= {1,1,2,2} and x2(n)=

{1,2,3,4} using DFT.10 Obtain X(k) for the sequence x(n)= {1,2,3,4,4,3,2,1} using Decimation-in-Time(DIT) , Fast

Fourier Transform(FFT) Algorithm.

11 Find the exponential form of the Discrete Fourier Series representation of x(n) if

12 Define Discrete Fourier Transform(DFT) and Inverse Discrete Fourier Transform(IDFT). Alsostate the Complex Conjugate property and Circular Convolution property of Discrete Fourier

Transform(DFT).

13 Consider two periodic sequences x(n) and y(n) with period M and N respectively. The sequence

w(n) is defined as w(n)= x(n)+y(n). Show that w(n) is periodic with period MN. (Hint : Using

DFT).

14 Obtain X(k) for the sequence x(n)= 2n

using Decimation-in-Frequency(DIF) , Fast Fourier

Transform(FFT) Algorithm.

Unit VI:

1 State the advantages of Digital filters.

2. Explain the effects of windowing. Define Rectangular and Hamming window functions.

3. Explain the procedure for designing an FIR filter using Kaiser window.

4. What is bilinear transformation? Apply bilinear transformation to with T=0.1 s.5. Describe the Inverse Chebyshev filters.

6. Obtain the system functions of normalized Butterworth filters for order N = 1 & 2.

7. What are the advantages of FIR filter over IIR filters?

8. What is an IIR filter? Compare its characteristics with an FIR filter.

9. Write note on Butterworth filters.10. Write note on Chebyshev filters.

11. Describe elliptical filters in detail.