**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 : [10]

i) y(n) = x^{2}(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. [8]

OR

Q2) a) Find linear convolution of following sequences using matrix or tabular method. [10]

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. [8]

Q3) a) State and prove following properties of z- transform. [6]

i) Linearity.

ii) Time shifting.

iii) Scaling.

b) Find the inverse z-transform using partial fraction method [10]

, , 1 + 3z^{-1} x( z) =1 + 3z^{-1} + 2 z^{– }^{2} For

i) ROC |z| > 2

ii) ROC |z| < I

OR

Q4) a) Explain following properties of Discrete Time F ourier Transform (DTFT) [6]

i) Linearity.

ii) Time shifting.

iii) Frequency shifting.

b) Determine the z-transform and the ROC of the signal [10]

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

^{t}yp^{es}– ^{[V]}

b) Explain frequency response of rational systems. [8]

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. [10]

b) Explain the concept of phase distortion and group delay. [6]

SECTION – II

Compute 4-point DFT of the sequence x(n) = {0, 1, 2, 3} [8]

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

OR

Compute circular convolution of following sequence using matrix approach [10]

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. [6]

i) Periodicity.

ii) Linearity.

Give difference between analog and digital filters. [6]

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

H(e^{jw}) = 1 for — <10) I < —1 3= 0 otherwise

Using rectangular window for length M = 5 [12]

OR

Give difference between FIR and IIR filter. [8]

The system function of the analog filter is given by

u( \ = ^{s} + ^{0}–^{1} = (s + 0.1)^{2} +16

Obtain system function of the digital filter using bilinear transformation

. . n

which is resonant at w_{r} = . [10]

Lu

Draw Direct form – II structure of following systems. [10]

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. [6]

OR

Explain with block diagram application of DSP in power factor correction. [8] Explain with block diagram application of DSP in harmonic analysis. [8]

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