Question Paper: Digital Signal Processing Question Paper - Dec 17 - Computer Engineering (Semester 7) - Mumbai University (MU)
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## Digital Signal Processing - Dec 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 microprocessor with digital signal processor.
(5 marks) 00

1(b) State whether x[n]=cos(3$\pi$n/4) is an energy or power signal with proper justification.
(5 marks) 00

1(c) Find the cross correlation of two causal sequences x[n]= {2,3,1,4} and y[n]= $3\delta(n-3)-2\delta(n)+\delta(n-1)+4\delta(n-2)$
(5 marks) 00

1(d) State BIBO stability criterion for LTI systems. Test the stability of the LTI systems, whose impulse response is: h[n] = 0.2$^n$u[-n]+3$^n$u[-n].
(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) Consider analog signal x(t) = 2sin80$\pi$t. If the sampling frequency is 60Hz, find the sampled version of discrete time signal x[n] also find an alias frequency corresponding to Fs = 60Hz.
(10 marks) 00

3(a) Determine the output response of the LTI system using tabular method, whose input is:

• x[n] = 1 ; n = 0,1
• x[n] = 3 ; n = 2,3
• x[n] = 0 ; elsewhere and h[n] = $\delta[n]-2\delta[n-1]+3\delta[n-2]-4\delta[n-3]0$.
(10 marks) 00

3(b) Compute DFT of sequence x[n] = {0,2,3,-1}. Sketch the magnitude and phase spectrum.
(10 marks) 00

4(a) Explain the following properties of DFT:

• i) Periodicity
• ii) Linearity
• iii) Time Shift
• iv) Circular Convolution
• v) Time Reversal
(10 marks) 00

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

5(a) In a LTI system the input x[n] = {1,2,1} and impulse response is h[n] = {1,3}. Determine the response of LTI system using radix-2 DIT FFT method.
(10 marks) 00

5(b) Explain Parseval's energy theorem.
If IDFT { X(k) } = x[n] = {2,1,2,0} using DFT properties, evaluate the following:

• i) IDFT of { X(k-1) }
• ii) IDFT of { X(k) circularly convolved with X(k) }
• iii) IDFT of { X(k).X(k) }
• iv) Signal energy
(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] = {3,4,7,8} and y[n] = {2,1,1,2}.
(10 marks) 00

6(b)

• i) Compare 64 point DFT and FFT systems with respect to the number of complex additions and multiplications required.
• ii) Write a detailed note on biomedical applications of DSP processors.
(10 marks) 00