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Discrete Time Signal Processing : Question Paper May 2015 - Electronics & Telecomm. (Semester 6) | Mumbai University (MU)

## Discrete Time Signal Processing - May 2015

### Electronics & Telecomm. (Semester 6)

TOTAL MARKS: 80
TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.
(2) Attempt any three from the remaining questions.
(3) Assume data if required.
(4) Figures to the right indicate full marks.
1 (a) Sketch the frequency response and identify the following filters based on their pass band $$i) \ h [n] = \left \{ 1, - \dfrac {1}{2} \right \} \\ ii) \ H[z] = \dfrac {z^{-1}-a}{1-az^{-1}}$$(5 marks) 1 (b) Justify DFT as a linear transformation.(5 marks) 1 (c) Explain the frequency warping in Bilinear transformation.(5 marks) 1 (d) What is multi rate DSP? Where it is required?(5 marks) 2 (a) An analog filter has transfer function $$H(s) = \dfrac {s+0.1}{(s+0.1)^2 +16}$$ Determine the transfer function of digital filter using bilinear transformation. The digital filter should be have specification $$\omega_r = \dfrac {\pi}{2}$$(8 marks) 2 (b) Explain the effects of coefficient quantization in FIR filters.(8 marks) 2 (c) The first point of eight point DFT of real valued sequence are {0.25, 0.125-j0.3018, 0, 0.125-j0.518, 0}.
Determine the remaining three points.
(4 marks)
3 (a) $$x[n] = \left\{\begin{matrix} 1, &0 \le n \le 3 \\0, &4 \le n \le 7 \end{matrix}\right.$$ i) Find DFT X[k]
ii) Using the result obtained in (i) find the DFT of the following sequences. $$x_1 [n] = \left\{\begin{matrix} 1, &n=0 \ \ \ \ \\0, &1 \le n \le 4 \\ 1, & 5 \le n \le 7 \end{matrix}\right. \ and \ x_2[n] = \left\{\begin{matrix} 0, &0\le n \le 1 \\ 1, &2 \le n \le 5 \\ 0, & 6 \le n \le 7 \end{matrix}\right.$$
(10 marks)
3 (b) Implement a two stage decimator for the following specifications. Sampling rate of the input signal=20,000 Hz,
M=100
Pass band=0 to 40 Hz, Pass band ripple=0.01,
Transition band=40 to 50 Hz, Stop band ripple=0.002
(10 marks)
4 (a) By means of FFT-IFFT technique compute the linear convolution of x[n]={2,1,2,1} and h[n]={1,2,3,4}.(8 marks) 4 (b) Consider the following specification for a low pass filter
0.99 ≤ H(e)1≤1.01
0≤ω≤0.3 Π and
1 H(e) 1 ≤ 0.01
0.5 Π ≤ 1 ω 1 ≤ Π
Design a linear phase FIR filter to meet these specification using the window design method.
(8 marks)
4 (c) Identify whether the following system is minimum phase, maximum phase, mixed phase.
i) H1(z)=6+z-1-z-2
ii) H2=1 - z-1 - 6z-2.
(4 marks)
5 (a) Design digital FIR filter for following specification. Use hamming window and assume M=7. (10 marks) 5 (b) Design digital low pass IIR Butterworth filter for the following specifications:
pass band ripple ≤dB|dB
pass band edge: 4 KHz
stop band attenuation ? 40 dB
stop band edge: 6 KHz
sample rate: 24 KHz
Use bilinear transformation.
(10 marks)
6 (a) Write a short note on
i) Dual tone Multi-frequency Signal Detection
ii) Different methods for digital signal Synthesis.
(12 marks)
6 (b) The transfer function of digital causal system is given as follows: $$H (z) = \dfrac {1-z^{-1}}{1-0.2z^{-1}-0.15z^{-2}}$$ Draw cascade form, parallel form realization.(8 marks)

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