**B.E. (Electrical)**

**DIGITAL SIGNAL PROCESSING**

**(2003 Course) (Elective – II) (403150) (Sem. – II)**

Time : 3 Hours

*Max. Marks : 100*

Instructions to the candidates:

1) Answer three questions from Section – I and three questions from Section – II.

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

3) Neat diagrams must be drawn wherever necessary.

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

5) Assume suitable data, if necessary.

SECTION – I

Q1)

a) State and explain sampling theorem and nyquist rate.

b) Compute linear convolution by tabulation method :

i) X (* n*) =

*+ 1 for 0 ≤*

*n**n*≤1= 5 –

*for 2 ≤*

*n**n*≤ 4= 0 elsewhereH (

*) = –*

*n**/2 for 2 ≤*

*n**n*≤ 4= 0 elsewhere

ii) X (* n*) = {2, 2, 2}h(

*) = {1, 2, 3, 2, 1}↑*

*n*c) State advantages of digital signal processing over analog signal processing.

[6]

OR

Q2)

a) Explain properties of linear convolution.

b) Obtain the cross correlation for the DT sequence given below and sketch

result X (n) = {2, – 1, 3, 7, 1, 2, – 3} Y (n) = {1,– 1, 2, – 2, 4, 1, – 2, 5}↑ ↑

c) Determine whether the given systems are static/dynamic, linear/ nonlinear

i) Y (* n*) =

*e*(

*x**) ii) Y (*

*n**) =*

*n**(*

*x**) +*

*n**(*

*n x**– 2)*

*n*

Q3)

a) How causality and stability is determined in terms of Z transform.

b) Determine z transform and ROC of following :

i)* x *(

*) = 2*

*n**n+2*(

*u**– 1)*

*n*ii) * x *(

*) =*

*n**2*

*n**(*

*u**)*

*n*OR

Q4)

a) Obtain inverse z transform using residue method.

(3)( 1)( 2)24 5− − −= − +z z zz z zX z

b) State and prove initial and final value theorem and obtain the final value

of ( ) ( 0.5)( 0.2)( 1)2.4− + −=z z zzx z

Q5)

a) State and prove any four properties of DFT.

b) Calculate DFT of * x*(

*) = {1, 1, 0, 0} check answer by calculating IDFT.*

*n*OR

Q6)

a) Explain radix-2 DIF FFT algorithm for computation of DFT when N = 8.

b) Find linear convolution of following sequence and obtain same result using circular convolution.

X 1 (* n*) = {1, 2, 3, 4} X 2 (

*) = {1, 1, 1}*

*n*

SECTION – II

Q7)

a) For the given difference equation develop cascade form and parallel form realization.

y(* n*) – (5/8)

*(n – 1) + (1/16)*

*y**(*

*y**– 2) =*

*n**(*

*x**) + (3/4)*

*n**(*

*x**– 1) + (1/8)*

*n**(*

*x**– 2)*

*n*b) Explain design of rectangular window method.

OR

Q8)

a) State advantages and disadvantages of digital filter over analog filter.

b) The transfer function of analog notch filter is given below, design the digital IIR notch filter using BLT with notch frequency 60 Hz and sampling frequency 960 sps.

( )1122+ += +s ssH s

Q9)

a) Explain Harward and modified Harward architecture of DSP and compare.

b) Explain ADSP 2100 series architecture of DSP with the help of major blocks and function of respective blocks.

OR

Q10)

a) Compare DSP processor over microprocessor.

b) For TMS 3200 c5x explain with neat block diagram its architecture.

Q11)

Write short note on :

a) Induction motor control using DSP.

b) Harmonic analysis using DSP.

OR

Q12)

Write short note on :

a) Power factor correction using DSP.

b) Vibration Analysis using DSP.