Question Paper: Digital Signal Processing & Processors Question Paper - December 2015 - Electronics Engineering (Semester 6) - Mumbai University (MU)
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## Digital Signal Processing & Processors - December 2015

### MU Electronics Engineering (Semester 6)

Total marks: --
Total time: --
INSTRUCTIONS
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary
1 (a) Justify: In impulse invariance transformation method there is many to one mapping of poles from s-plane to z-plane. 5 marks

1 (b) Find the number of computations required to compute 32 point DFT using direct calculation and by using FFT algorithm. Also find the computational complexity. 5 marks

1 (c) Compare DSP processor and microprocessor. 5 marks

1 (d) Compare fixed point arithmetic and floating point arithmetic. 5 marks

2 (a) Find the DFT of the following sequence using Radix 3 DIF FFT algorithm
x(n)={1, 2, 3, 4, 4, 3, 2, 1}
5 marks

2 (b) Compute the circular convolution of the sequence using DFT and IDFT approach
x1(n)={1, 2, 0}
x2(n) = {2, 2, 1, 1}
5 marks

3 (a) Design a Low pass FIR filter with 11 coefficients for the following specifications. Passband frequency edge = 0.25 KHz and sampling frequency=1KHz.
Use rectangular window in the design.
5 marks

3 (b) Explain frequency sampling method of designing FIR filter. 5 marks

4 (a) Use bilinear transformation to obtain a digital filter of notch frequency 75Hz and sampling frequency of 200Hz, for a given normalized second order filter having transfer function H(S)=S2+1S2+S+1H(S)=S2+1S2+S+1 H(S) = \dfrac {S^2 +1}{S^2 + S+1} 5 marks

4 (b) Design a Butterworth lowpass filter to meet the following specifications.
Passband gain = 0.89
Passband frequency edge = 30Hz.
Attenuation = 0.20.
Stopband edge = 75Hz.
5 marks

5 (a) Explain with neat diagram architecture of TMS320C67XX DSP processor. 5 marks

5 (b) Explain the applications of the DSP processor in following fields.
ii) Speech recognition.
5 marks

6 (a) Draw the quantization noise model for second order system <mi>H</mi><mo stretchy="false">(</mo><mi>z</mi><mo stretchy="false">)</mo><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>1</mn><mrow><mn>1</mn><mo>−</mo><mn>2</mn><mi>r</mi><mi>cos</mi><mo>⁡</mo><mi>θ</mi><msup><mi>z</mi><mrow class="MJX-TeXAtom-ORD"><mo>−</mo><mn>1</mn></mrow></msup><mo>+</mo><msup><mi>r</mi><mn>2</mn></msup><msup><mi>z</mi><mrow class="MJX-TeXAtom-ORD"><mo>−</mo><mn>2</mn></mrow></msup></mrow></mfrac></mstyle>[/itex]" role="presentation" style="font-size: 125%; text-align: center; position: relative;">H(z)=112rcosθz1+r2z2<math xmlns="https://www.w3.org/1998/Math/MathML" display="block"><mi>H</mi><mo stretchy="false">(</mo><mi>z</mi><mo stretchy="false">)</mo><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>1</mn><mrow><mn>1</mn><mo>−</mo><mn>2</mn><mi>r</mi><mi>cos</mi><mo>⁡</mo><mi>θ</mi><msup><mi>z</mi><mrow class="MJX-TeXAtom-ORD"><mo>−</mo><mn>1</mn></mrow></msup><mo>+</mo><msup><mi>r</mi><mn>2</mn></msup><msup><mi>z</mi><mrow class="MJX-TeXAtom-ORD"><mo>−</mo><mn>2</mn></mrow></msup></mrow></mfrac></mstyle>[/itex]<script type="math/tex; mode=display" id="MathJax-Element-2"> H(z) = \dfrac {1}{1-2r\cos \theta z^{-1} + r^2 z^{-2}} </script> find the steady state output noise variance. 5 marks

### Explain the following terms.

6 (b) (i) Dead band 5 marks

6 (b) (ii) Limit cycle oscillations. 5 marks

6 (b) (iii) Addressing modes of TMS320C67XX processor. 5 marks