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## Digital Signal Processing - Dec 2014

### Computer Engineering (Semester 7)

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)** Explain classification of Discrete systems.(5 marks)
**1 (b)** Prove that DFT is orthogonal transform.(5 marks)
**1 (c)** Explain image fidelity criteria.(5 marks)
**1 (d)** Unit step signal is a power signal. Justify.(5 marks)
**2 (a)** Check whether the following systems are linear/nonlinear and Time variant/Time invariant.

i) y(n)=e^{x(n)}

ii) y(n)=n x(n)(10 marks)
**2 (b)** Find the Z-transforming signals and sketch ROC. $$ i) \ x(n) = \left ( \dfrac {1}{4} \right )^n u (n) \\ ii) \ x(n) = \left ( \dfrac {1}{2} \right )^n u(-n-1) $$(10 marks)
**3 (a)** Explain Decimation is time FFT algorithm with signal flow graph.(10 marks)
**3 (b)** Determine circular convolution of two sequences

x_{1}(n)={1,2,3,1}

x_{2}(n)={4,3,2,2}(10 marks)
**4 (a)** Explain region based image segmentation techniques.(10 marks)
**4 (b)** Explain image enhancement techniques in spatial domain.(10 marks)
**5 (a)** Explain various types of redundancies in an image. Specify techniques to remove redundancies.(10 marks)
**5 (b)** Construct improved gray scale quantization code for given data

{100, 110, 124, 124, 130, 110, 200, 210}(10 marks)
**6 (a)** Explain trimmed average filtering and median filtering with example.(10 marks)
**6 (b)** Compute DFT of the given image

(10 marks)

### Write short notes on any four:

**7 (a)** Hough transform(5 marks)
**7 (b)** Histogram Equalization(5 marks)
**7 (c)** Wiener filter(5 marks)
**7 (d)** Noise models(5 marks)
**7 (e)** Walsh Hadamard Transform.(5 marks)