Question Paper: Digital Signal Processing Question Paper - May 17 - Computer Engineering (Semester 7) - Mumbai University (MU)
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## Digital Signal Processing - May 17

### Computer Engineering (Semester 7)

Total marks: 80
Total time: 3 Hours
INSTRUCTIONS
(1) Question No. 1 is compulsory.
(2) Attempt any three from remaining five questions.
(3) Assume suitable data if required.
(4) Figures in brackets on the right hand side indicate full marks.

1(a) Compare IIR systems with FIR systems.
(5 marks) 00

1(b) State whether x[n] = sin(n $\pi$/3) is an energy or power signal with proper justification.
(5 marks) 00

1(c) If x[n] = {1,2,2,1,3,1} is a periodic signal. Plot it in circular representation for-

• i) x[-n]
• ii) x[n-2]
• iii) x[n+2]
• iv) x[-(n-2)]
• v) x[-(n+2)]

(5 marks) 00

1(d) State BIBO stability criterian for LTI systems. Determine the range of values of 'p' and 'q' for the stability of LTI system with impulse response:

• h[n] = p$^n$ ; n<0
• h[n] = q$^n$ ; n>=0

(5 marks) 00

2(a) Check whether the system y[n] = a$^n$u[n] is:

• i) Static or Dynamic
• ii) Linear or Non-linear
• iii) Casual or Non-casual
• iv) Shift variant or shift Invariant

(10 marks) 00

2(b) Check the periodicity of the following signals and if periodic, find their fundamental period.

• i) cos(n/6).cos(n$\pi$/6)
• ii) sin(2$\pi$n/3)+cos(2$\pi$n/5)

(10 marks) 00

3(a) Determine output response of the LTI system using time domain method, whose input is x[n] = $3\delta[n+1]-2\delta[n]+\delta[n-1]+4\delta[n-2]$and h[n] = $2\delta[n-1]+5\delta[n-2]+3\delta[n-3]$.
(10 marks) 00

3(b) If a continuous time signal x(t) = sin(2$\pi$* 2000t)+2sin(2$\pi$*1000t) is sampled at 8000 samples/sec. Find out the 4-point DFT of it. Sketch the phase and magnitude spectrum.
(10 marks) 00

4(a) Explain any five properties of DFT
(10 marks) 00

4(b) Compute linear convolution of the casual sequences x[n] = {2,-3,1,-4,3,-2,4,-1} and h[n] = {2,-1} using overlap save method.
(10 marks) 00

5(a) Compute circular convolution of the casual sequences x[n] = {1,-1,1,-1} and h[n] = {1,2,3,4} using radix -2 DIT FFT method.
(10 marks) 00

5(b) If the DFT of x[n] is X(k) = { 2,-3j,0,3j } using DFT properties, find:

• i) DFT of x[n-2]
• ii) Signal energy
• iii) DFT of x*[n]
• iv) DFT of x$^2$[n]
• v) DFT of x[-n]

(10 marks) 00

6(a) Explain the significance of Carl's Correlation Coefficient Algorithm in digital signal processing. Evaluate Carl's Coefficient for two casual sequences x[n] = {2,4,4,8} and y[n] = {1,1,2,2}
(10 marks) 00

6(b)

• i) Calculate the percentage saving in calculations in a 64 point radix-2 FFT systems with respect to the number of complex additions and multiplications required, when compared to direct DFT system.
• ii) Write a detailed note on DSP processor.
(10 marks) 00