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.

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

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

**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].

**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)**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.

**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] = $\delta[n]-2\delta[n-1]+3\delta[n-2]-4\delta[n-3]0$.

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

**4(a)**Explain the following properties of DFT:

- i) Periodicity
- ii) Linearity
- iii) Time Shift
- iv) Circular Convolution
- v) Time Reversal

**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.

**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.

**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

**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}.

**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.