b. Ihe above decimator is to be designed as a two stage structure (M=6 MIM2, where ۸۱

= 10 and M2 2). Compare the computational complexity of single-stage decimator
design with that of the two-stage decimator design. Use the total multiplications per
second 95 9 measure of the computational complexity.

a. State and prove the noble identities of multi-rate systems. 4 0. In a 2 channel alias

free Quadrature Mirror Filter bank, one of the filter is 5 given by Ho(z) = 12 + 42-14 102
-2 + 22- + 22 -4 . Determine the remaining filters and find the transfer funcHon. Draw
the polyphase representation of the filter bank.

PART B

a. What are the limitations of Fourier Transform? How it is overcome in Short 3
Time Fourier Transform?

Consider a function f(t) G VI, where VI = Spank (8 (21 — k)) ; Let the 6 coefficients of
the basis functions of Vlfor f (t) = (3, 5, 2, 6, ೦. -2, 2, 4}, where g(t) corresponds to
Haar scaling function. (i) Can you express f(t) in terms of

basis functions of Vo, where Vo = Spank (@(t — k)). Justify your answer. (ii)
Express f(t) in terms of basis funcHons of % and Wo where Wo = Spank

(८ ~ k)}. Write the relation between Vo , Wo and VI.

Design Daubechies Orthogonal Wavelet system with two vanishing moments using 9 time
domain approach.

a. Obtain two level Discrete Wavelet Transform of the sequence x(n) = (3, 5, 2, 6, 5 0, —2,
2, 4) using normalized Haar wavelet implemented with Mallat Algorithm.

Check whether the following funcHon is an admissible wavelet. . 4
(೧-1-೧3
PART C

Derive the Mallat Filterbank structure (Analysis & Synthesis) for a Biorthogonal 12 Wavelet
System starting from the basic two scale equations.

a. Differentiate between an orthogonal wavelet system and biorthogonal wavelet
4system.

b. Draw the Haar wavelet packet basis for three levels of decomposition. 4

4.
b.
5.
6.
b.
7.
8.
6
9.

What are the advantages of Wavelet Packet Transform over Wavelet 4
Transform?

12
Obtain two level Discrete Wavelet Transform of the following sequence with

normalized Haar Wavelet using lifting scheme.
Data [34, 36, 36, 40, 38, 34, 34, 441