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.

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

**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)]

**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

**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

**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)

**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] = $2\delta[n-1]+5\delta[n-2]+3\delta[n-3]$.

**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.

**4(a)**Explain any five properties of DFT

**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.

**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.

**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]

**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}

**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.