PART 13

a. Show the time-frequency tiling of Short Time Fourier Transform (SIFT) and Discrete 5 Wavelet
Transform (WT). Explain how wavelet transform try to overcome the limitations imposed by

Heisenberg's uncertainty principle in time frequency analysis.

0. — . Write a note on multiresolution analysis. Check whether Haar wavelet can be used for 4

multiresolution analysis.

a. Prove that the spaces spanned by scaling function bases are nested and the spaces 5 spanned by

wavelet function bases are orthogonal among themselves in Haar decomposition

0. Asignal in V2 space 15 given (7)5 [4,8,2,-6,2,4,2,6) asx(n)= 4
Perform Haar decomposition into V4,W ,Vo and Wo 080൦5.

Find the wavelet coefficients W(a,b) for the signal f(t) for )0. Use Haar 5

wavelet
1ಎ (1, 055 1
0, otherwise
b. How wavelet transform can be used in the compression of image data? Show the filter 4 bank

structure for image decomposition.

PART ^
a. Explain LMS algorithm for optimum design of an adaptive filter. Give proper equations 6

and derivations.

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Explain Periodogram analysis for power spectrum estimation. 6

a. Explain Yule-Walker method for Power spectrum estimation. 6

b. Give the steps involved in Blackman and Tukey method of Power spectrum estimation. 6

a. Obtain the normal equations for the m-step linear predictor? 6

b. Explain how Levinson-Durbin algorithm can be used to solve the normal equations 6
recursively.