National Institute of Technology 2007-7th Sem B.Tech Electronics and Communications Engineering EC 455T Wavelets--ember - Question Paper

NATIONAL INSTITUTE OF TECHNOLOGY, CALICUT
Seventh Semester B.Tech End Semester Examination- November 2007
EC 455T Wavelets

Answer AH Questions

Check whether the following functions are admissible wavelets?

1. (1 - 2t² )e ^-

2. e^-t Cos

0 t < 0 t 0 < t < 1 1 t >1

Show that the wavelet transform of F(t) using Haar Wavelet is

2F(b + ) - F(b) - F(b + a)

W(a,b) = sgn(a)-

Design a Filter bank to compute the 4 point DFT of a Digital Sequence. Obtain DFT of the following sequence using the above filter bank. x(n) = { 4, 8, 4, 10 }

III a)

b)    Obtain 1 level DWT of the above sequence using Haar Wavelet implemented with Mallat Algorithm.

c)    Compare the performance of the two transforms in terms of energy compaction.

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

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

How will you get time information from Mallats structure?

VI    What are the advantages of Wavelet Packet Transform compared to Wavelet Transform? How will you determine the best wavelet packet bases for a given data?

VII Distinguish between Time Domain Masking and Frequency Domain Masking in the context of hearing process , with necessary diagrams.

IX For the seven-level decomposition shown below,

21	6	15	12
-6	3	6	3
3	-3	0	-3
3	0	0	0

^a)    Find the bit stream or labels generated by the Embedded Zerotree Wavelet (EZW) coder, after three steps of significant and refinement passes. Also, determine the list of significant coefficients.

b)    Find the Mean Squared Error between the original DWT coefficients and reconstructed coefficients after three passes.

X Write short notes on :

a)    Regularity of a wavelet

b)    Vanishing Moments of a wavelet

c)    Admissibility condition

d)    Multi-resolution property of wavelet systems

XI a) Obtain two level DWT of the following sequence using Haar Wavelet Transform with lifting scheme.

10, 20, 25, 15, 20, 15, 10, 15

b)    Compare the computational complexities of Mallat algorithm & Lifting scheme for this case in terms of total number of multiplications and

_c)    additions.

Compute the energy stored in the four low frequency sub-bands.

d)

Threshold few coefficients and perform inverse DWT using Lifting scheme such that the reconstructed sequence retains approximately 90% of the total energy of the original sequence.

[marks3]

Attachment: national-institute-of-technology-2007-b-tech-electronics-and-communications-engineering-5917-1.pdf

Earning:   Approval pending.