UNIV4VINU | ENGINEERING ACHIEVERS

DIGITAL SIGNAL PROCESSING

PART-A (10 x 2 = 20 Marks)

1. Differentiate between analog and digital signal. Why Digital signal processing is widely

used than analog signal processing.

2. State Shannon’s Sampling theorem.3. Determine the Z-transform of (1/2)n[ u[n]-u[n-

8]] and indicate its ROC.

4. Compare FIR and IIR filter.

5. What are the advantages of linear phase characteristics? Which systems exhibit linear

phase?

6. Show that the system described by the difference equation is an all pass system3 y(n) –

y(n-1) = -x(n) + 3x(n-1)

7. Mention few application areas where speech coding is required.

8. Explain the circular addressing mode of DSP processor

9. Find the DFT of the signal x(n)= {1,3,5,7}.

10. Distinguish between recursive and non-recursive realizations of filters.

PART-B (5x16 = 80 Marks)

11.i) Show that Z-Transform of x*(n) is X*(z*). (4)

ii) Consider a linear shift-invariant discrete system with input x(n) and output y(n) for

whichy(n-2) – 2.5 y(n-1) +y(n) =x(n)By considering the pole-zero pattern associated with

the difference equation, determine the three possible choices for the unit-sample

response of the system. Comment on the stability of the system in each case. (12)

12.a)i) Find the DFT of the sequence {1,1,1,1,2,2,2,2} using radix-2 Decimation-in-Time

FFT. Sketch the magnitude and phase plot. (12)

ii) What is the need for FFT? (4)

(OR)

12.b)i) Find the DFT of the sequence {1,1,1,1,2,2,2,2} using radix-2 Decimation-in-

Frequency FFT. (12)

ii) Write about over lap save method. (4)

13.a) The specification of the desired low pass filter are:Amin = 22 dB and Amax = 3 dB ?p

= 0.2? and ?s = 0.4?Design a Butterworth digital filter using Bilinear Transformation. (Amin

and Amax are attenuation) (16)

(OR)

13.b) Design and also realize a high pass FIR filter with a cutoff frequency of 1.3 rad/sec

and N=9. (16)

14.a)i) Perform the linear convolution of (1/4)n u(n) and (1/2)n u(n). (6)

DIGITAL SIGNAL PROCESSING

PART A – (10 X 2 = 20 marks)

1. State Sampling Theorem?

2. Find the Poles of the system.

3. Find the DFT of the sequence x(n) ={1, 1, 0, 0 } DFT is obtained by FFT.

4. Calculate the number of multiplications needed in the calculation of 512 point

radix2FFT when compared to Direct DFT?

5. What are the properties that are maintained same in the transfer of analog filter into

adigital filter?

6. What is warping effect?

7.Draw the direct from realization of FIR system?

8.What are the describe features of a window function? Name the different types

ofwindowing function?

9. What is truncation?

10. Draw a sample/ hold circuit and explain its operations?

PART B – (5 X 16 = 80 marks)

11. (a) (i) For each of the following discrete time system, determine whether or not

thesystem is Linear Time, Variant, Causal and Stable?

11.(a) (ii) Determine the transfer function, magnitude & phase response, impulseresponse

for the system.

11. (b) (i) Find the Ztransformof1) x(n) = 2 n u (n2)2) x(n) = n 2 u (n)

11.(b)(ii) Use convolution to find x(n), given

11.(b) (iii) Determine the cross correlation values of the sequence x1(n) ={ 1, 2, 3, 4

}x2(n) = {4, 3, 2, 1}12. (a) (i) Compute linear and circular convolution of the two

sequencex1(n) ={ 1, 2, 2, 2 } and x2(n) = {1, 2, 3, 4}

12.(a) (ii) Compute the FFT using DIT algorithm for the sequence x(n) = {1, 2, 3, 4, 4, 3,2,

1 } and draw the corresponding flow diagram.

12.(b) (i)Prove that multiplication DFT’s of 2 sequence is equivalent to the DFT of

thecircular convolution of the 2 sequence in time domain?

12.(b)(ii) Discuss in detail the use of FFT algorithm , in linear filtering?

13.(a) Find H(z) using impulse invariant technique for the analog system function.

13 (b) (i) Obtain the direct form II, Cascade form parallel form structures for the system?

DIGITAL SIGNAL PROCESSING,

PART – A (10 X 2 = 20 MARKS)

1. State and prove the convolution property of Z transform.

2. Check the system is linear or not y(n) = x(n)+ay(n-1)

3. Write equations for finding DFT and IDFT using Z transform.

4. Draw the radix 2 butterfly structure for DIF

5. Draw the implementation for the generalized for IIR filter using direct form II.

6. Explain how the addition and multiplication of (H1, H2) impulse responses

implemented in filter design

7. Write equations for Hanning and Blackman window.

8. Why frequency prewarping procedure is adopted in the design of IIR filter?

9. Write two advantages of musical sound processing and briefly explain.

10. Explain the effects due to upsampling.

PART - B (5 x 16 = 80 Marks)

11.i) The impulse response of a linear TI system is h(n) = {1, 0, 1, -1}. Find the response

of the system to the input signal x(n) = {1, 0, 2, 1}.

ii) Check whether the system y(n) = x(n) – x(n-1) is LTI and stable.

12.a) Develop and draw the 8 point radix-2 DIT FFT algorithm for DFT computation.

(OR)

12.b) Compute the DFT of the following sequence x(n) = 0 0£ n £ 2= 1 3£ n £ 6= 0 n=7 Plot

magnitude and phase spectra

13.a) Design a LPF with following specifications. Use Hamming window and at least 8

points.

(OR)

13.b)i) Obtain H(z) from H(s) when T = 1 sec.

ii) Design a digital BPF using w1 & w2 as cutoff frequencies

14.a)i) Perform the following using Floating Point arithmetic.1.5 x 1.75 and 1.5 x 1.75

ii) Realize the following H(z) given byusing cascade and Parallel form with Direct form-I.

(OR)

14.b)i) What is meant by quantization error? Explain briefly.

ii) Realize the following filter using cascade technique with DF-I and DF-II.

15.a) Briefly explaina. Interpolatorb. Decimatorc. Effects due to sampling rate conversion

(OR)

15.b)i) Write a note on Musical sound processing