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## Digital Signal Processing - Dec 2013

### 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.

### Justify/Contradict the following statement (any four) :-

**1 (a) (i)** Unit step sequence is a powersignal(5 marks)
**1 (a) (ii)** If the energy of the signal is finite its power is zero(5 marks)
**1 (a) (iii)** Brightness discrimination is poor at low levels of illumination(5 marks)
**1 (a) (iv)** Enhacement process does not add any information to the image.(5 marks)
**1 (a) (v)** All image compression techniques are invertible.(5 marks)
**2 (a)** Write an expression for 2-D DFT. What is its relationship with one dimention DFT? How one-dimensional FFT algorithm can be used to compute two dimensional DFT of an digital image.(10 marks)
**2 (b)** Define signals and systems and also give any 4 classification of Discrete Time Signals with examples.(10 marks)

### Compare and constrast between the following (any two -)

**3 (a) (i) ** Spatial Domain Processing and Transform Domain Processing.(5 marks)
**3 (a) (ii)** Image Enhancement and Image Restoration.(5 marks)
**3 (a) (iii)** Lossless and Lossy Compression(5 marks)
**3 (b)** Find the DFT of the given image.

**3 (c)**Find the circular convolution of two sequence -

x

_{1}(n)={1,-1,2,-4} and x

_{2}(n)={1,2}(5 marks)

**4 (a)**Find the universe Z-transform of -

$$x\left(z\right)=\frac{z^3-4z^2+5z}{\left(z-1\right)\left(z-2\right)\left(z-3\right)}$$

(i) ROC=|z|>3

(ii) ROC=|z|<1

ROC=2<|z|<3

(10 marks)

**4 (b)**What are the different types of redundancies in images.(5 marks)

**4 (c)**Explain Fidelity Criteria(5 marks)

**5 (a)**Explain filtering in spatial Domain.(10 marks)

**5 (b)**Explain segmentation based on discontinuities.(5 marks)

**5 (c)**Explain Hough-Transform and its application in detection of shapes.(5 marks)

**6 (a)**Explain the salient feature of the following codes :-

(i) Huffman code

(ii) Lossy predictive coding

(iii) Tranform coding. (10 marks)

**6 (b)**Explain with suitable example region splitting and merging techniques for segmentation.(10 marks)

**7 (a)**Sampling and Quantization.(5 marks)

**7 (b)**Edge linking and Boundry detection via graph theoretic technique.(5 marks)

**7 (c)**Image Restoration Model.(5 marks)

**7 (d)**Trimmed Average filter.(5 marks)

**7 (e)**Homomorphic filtering.(5 marks)