# Pune University BE Question Paper Digital Signal Processing

B.E. (Electrical) DIGITAL SIGNAL PROCESSING (2008 Pattern) (Elective – III) (Sem. – II)

Time :3 Hours]                                                                           [Max. Marks :100

Instructions to the candidates:-

1)            Answers to the two sections should be written in separate books.

2)            Neat diagrams must be drawn wherever necessary.

3)            Use of logarithmic tables, slide rule, Moillier charts, electronic pocket calculator and steam tables is allowed.

4)            Assume suitable data, if necessary.

5)            Solve Q.1 or 2, Q.3 or 4, Q.5 or 6 from Section I and Q.7 or 8, Q.9 or 10, Q.11 or 12 from Section II.

SECTION – I

QI) a) Few discrete time systems are given below :                                                      

i)            y(n) = x2(n)

ii)          y(n) = x(2n)

Check whether systems are

1)           Static or dynamic.

2)           Linear or Non – linear.

3)            Shift variant or invariant.

b) Explain classification of Discrete Time Signal.                                               

OR

Q2) a) Find linear convolution of following sequences using matrix or tabular method.   

i)               x(n) = I for n = -2,0,1= 2 for n = —1 = 0 otherwise h(n) = S(n) — S(n — 1) + S(n — 2) — S(n — 3)

ii)          x(n) = {1,1,0,1,1} for —2 < n < 2 h(n) = {1,—2,—3,4} for —3 < n < 0

b) Explain sampling theorem and anti – aliasing filter in A to D conversion. 

Q3) a) State and prove following properties of z- transform.                                        

i)             Linearity.

ii)           Time shifting.

iii)         Scaling.

b) Find the inverse z-transform using partial fraction method                        

, , 1 + 3z-1 x( z) =1 + 3z-1 + 2 z2 For

i)             ROC |z| > 2

ii)           ROC |z| < I

OR

Q4) a) Explain following properties of Discrete Time F ourier Transform (DTFT) 

i)             Linearity.

ii)           Time shifting.

iii)        Frequency shifting.

b) Determine the z-transform and the ROC of the signal                                 

i)               x(n) = [3.(4)n – 4.(2)n]u(n)

ii)            x(n) = {1,-2,1,3,4} for – 2 < n < 2

Q5) a) Explain Generalized Linear Phase System (GLPS) along with its four

types–                                                                                                                        [V]

b) Explain frequency response of rational systems.                                             

OR

Q6) a) A discrete time system has a unit sample response h(n) given by

h(n) = 1^(n) +S(n-1) + 1s(n- 2)

Find the system frequency response H(e,m) for – n < w < n in steps of —. Plot magnitude and phase response.                                                      

b) Explain the concept of phase distortion and group delay.                              

SECTION – II

Compute 4-point DFT of the sequence x(n) = {0, 1, 2, 3}                          

Explain 8-point Radix -2 DIT – FFT algorithm.                                            

OR

Compute circular convolution of following sequence using matrix approach        

i)               x(n) = {0,1,2,3,0,1,2,3} and h(n) = {1,11,1}.

ii)             x(n) = {3,2,1,0} and h(n) = {1,0,1,0}.

State and explain following properties of DFT.                                            

i)              Periodicity.

ii)           Linearity.

Give difference between analog and digital filters.                                      

Design the band – pass filter whose frequency response is given by

H(ejw) = 1 for — <10) I < —1                                        3= 0 otherwise

Using rectangular window for length M = 5                                               

OR

Give difference between FIR and IIR filter.                                                  

The system function of the analog filter is given by

u( \ = s + 01 = (s + 0.1)2 +16

Obtain system function of the digital filter using bilinear transformation

. .                                                                                n

which is resonant at wr = .                                                                               

Lu

Draw Direct form – II structure of following systems.                              

i)               y(n) + y(n -1) – 4yn(n – 3) = x(n) + 3x(n – 2)

3                                       1                                 1

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

4o                                                     2

Explain cascade form structure of IIR system.                                             

OR

Explain with block diagram application of DSP in power factor correction.  Explain with block diagram application of DSP in harmonic analysis. 

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