PART ^

8 (1. 05853
f(t) 0 ٥ئ‎ ٠۳۷۹۶ (6)

0) Obtain the 2 band polyphase decomposition of the filter with transfer function

H(z)= 1-3z- (3)

a) Decompose the signal x(n)= 4, 8, 2 ,6 -2, 4, 2, 6, 2,2 in VI space to its coarser components
in VO space using Haar Wavelet function (4) b) Sketch the filter bank implementation of

DWT with respect to signal decomposition(4)
c) How can a linear predictor implemented using FIR filter with lattice structure? (4)

a) Let Acos(oon+8) +e(n) where 9 is a random variable that is uniformly distributed on the
interval from 0 to 211 and e(n) is a sequence of zero-mean random variables that are
uncorrelated with each other and also uncorrelated with 8.

i) Find the ACF for x(n) if is variance ofe(n) . (2) மிப power spectrum of x(n) over
one period (2) iii) Explain periodogram analysis of the signal using Barlett method (3)

b) Determine the frequency resolution of the Barlett method of power spectrum
estimation for a quality factor 10 . The length ofthe sample sequence is 2000.
Comment on the result. (5)

Explain how Levinson Durbin algorithm can be used in
i) Design of forward linear predictor (6) ii) Design of power spectrum estimator using
Yule Walker method (6)

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