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## Digital Signal Processing - May 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)** Laplacian is not good edge detector. Justify.(5 marks)
**1 (b)** Discuss the properties of Region of Convergence.(5 marks)
**1 (c) ** Convolution in one domain leads to multiplication in other domain.(5 marks)
**1 (d)** Walsh transform is nothing but sequence Orderd Hadamard Transform Matrix Justify.(5 marks)
**2 (a)** Construct following gray scale quantization code for given level data set.

{100, 110, 124, 130, 200, 210}(10 marks)
**2 (b)** Find the following sequence are periodic or no. If yes, find the fundamental time period-

(i) x_{1}(n)=3sin(0.01 ?n)+4cos(10 n)

(ii) x_{2}=cos(0.01 ?n)

(10 marks)
**3 (a)** Determine the system function and unit sample response of the given system described by following difference equations :

$$y(n)= \frac{1}{4} y(n-2)+\frac{1}{2}y(n-1)+x(n)$$(10 marks)
**3 (b)** Find cross-correlation between given signals.

x(n)={1,0,1,2}

y(n)={1,2,3,4}

(5 marks)
**3 (c) ** Find auto-correlation of following signal

x(n)={1,1,2,3}(5 marks)
**4 (a)** Compute DFT of the given image using DIF-FFT technique

0 | 1 | 2 | 1 |

1 | 2 | 3 | 2 |

2 | 3 | 4 | 3 |

1 | 2 | 3 | 2 |

**4 (b)**Explain the process of image segmentaion using different methods.(10 marks)

**5 (a)**Specify DCT basis functions and construct transform matrix for an image.(10 marks)

**5 (b)**Obtain the digital negative of the following 8 bits per pixel image.

121 | 205 | 217 | 156 | 151 |

139 | 127 | 157 | 117 | 125 |

252 | 117 | 236 | 138 | 142 |

227 | 182 | 178 | 197 | 242 |

201 | 106 | 119 | 251 | 240 |

**6 (a)**Perform Histogram Equalization on the given image transform

Gray Level | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |

Number of Pixel | 70 | 100 | 40 | 80 | 60 | 40 | 08 | 02 |

**6 (b)**Write 8 x 8 Walsh transform matrix and draw its signal flow graph(10 marks)

### Write short noes on (any four) :-

**7 (a)** Hough transform(5 marks)
**7 (b) ** Wavelet Transform(5 marks)
**7 (c) ** Classify and define discrete time systems(5 marks)
**7 (d)** Homomorphic filtering.(5 marks)
**7 (e) ** State and prove convolution property of Z-transform.(5 marks)