Question Paper: Discrete Time Signal Processing Question Paper - May 17 - Electronics And Telecomm (Semester 6) - Mumbai University (MU)
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## Discrete Time Signal Processing - May 17

### Electronics And Telecomm (Semester 6)

Total marks: 80
Total time: 3 Hours
INSTRUCTIONS
(1) Question 1 is compulsory.
(2) Attempt any three from the remaining questions.
(3) Draw neat diagrams wherever necessary.

1(a) Derive relationship between DFT and DTFT.
(5 marks) 00

1(b) Compare: Impulsive invariant technique and bilinear transformation technique.
(5 marks) 00

1(c) Define phase delay and group Delay.
(5 marks) 00

1(d) Explain interpolation process with frequency spectrum.
(5 marks) 00

2(a) Develop Composite radix DITFFT flow graph for N=6=2X3
(10 marks) 00

2(b) Analog filter transform function is $H(S) = \frac{4}{(s+1)(s^2+4s+5)}$ obtain equivalent digital filter transfer function H(Z) using impulse invariant technique by taking T=0.5 sec.
(10 marks) 00

3(a) State two important properties of DFT which are used to derive FFT. How computational complexity of DITFFT algorithm is determined from flow graph. Derive necessary formulas.
(10 marks) 00

3(b) $$y(n) = 2x(n) + \frac{4}{5} x(n-1) + \frac{3}{2}x(n-2) + \frac{2}{3} x(n-3)$$

Determine lattice realization.

(10 marks) 00

4(a) Using frequency sampling method, design FIR band pass filter for following specifications

Sampling frequency = 800 Hz

Cut Off frequency = $f_{c2}$ = 3000 Hz

Cut Off frequency = $f_{c1}$ = 1000 Hz

Determine filter coefficients for N=7

(10 marks) 00

4(b) Write short note on: Dual tone multi frequency detection
(6 marks) 00

4(c) What is multi rate DSP? State its applications.
(4 marks) 00

5(a) Design a Butterworth digital IIR filter using BLT by taking T=0.1 sec to satisfy following specifications

$$0.6 \le |H (e^{jwr}) | \le 1.0 \space \space \space 0 \le w \le 0.35 \pi$$

$$|H (e^{jwr}) | \le 1.0 \space \space \space \space \space \space 0.7 \pi \le w \le \pi$$

(10 marks) 00

5(b) x(n) = {2,3,4,5} and y(n) = {5,2,3,4}

(i) Find circular convolution using time domain method

(ii) Find circular convolution using frequency domain method

(iii) Compute linear convolution. Comment on your results.

(10 marks) 00

6(a) The transfer function for discrete time causal system is given by $H(z) = \frac{1-z^{-1}}{1-0.2Z^{-1} - 0.15Z^{-1}}$

(i) Find difference equation

(ii) Draw Direct Form-I and Direct Form-II realization structure.

(iii) Draw cascade and parallel realization.

(10 marks) 00

6(b) Explain the effects of coefficients quantization in FIR filters.
(5 marks) 00

6(c) State Parserval's theorem. Verify it for x(n) = {1,2,3,4}
(5 marks) 00