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WAVELET TRANSFORMS AND 3712606

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Code: 3712606 Credits: 4 Semester 1 EAC(

Wavelet Transforms and Applications

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Wavelet Transforms and Applications Syllabus — Unit-wise Content

The official GTU curriculum for Wavelet Transforms and Applications (subject code 3712606) as prescribed for EAC( · Semester 1 divides the course into 7 units, covering 13 listed topics. The unit-wise breakdown below is read from the GTU syllabus document for this subject code, so you can check what the course actually covers before deciding which papers to attempt.

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Unit 1 Introduction

6 lecture hours

 Origin of wavelets and its history  Different communities of wavelet  Classification: continuous and discrete wavelet transforms  Developments in wavelet theory applications

Unit 2 Continuous Wavelet Transform

6 lecture hours

 Introduction  Continuous time wavelets  Definition of CWT  Constant Q factor filtering interpretation and Time Frequency Resolution  CWT as an operator  Inverse CWT

Unit 3 Introduction to the Discrete Wavelet Transform and orthogonal Wavelet decomposition

7 lecture hours

 Approximations of vectors in nested linear vector subspaces  Multi-resolution Analysis of L2( R)  Haar Scaling function  Haar wavelet  Haar wavelet decomposition.  Haar wavelet packets and application

Unit 4 MRA Ortho-normal wavelets and their relationships to filter banks

5 lecture hours

 Construction of an ortho-normal MRA  Wavelet basis for the MRA  Digital filtering interpretation  Examples of orthogonal basis generating wavelets  Interpreting ortho-normal MRA for discrete time signals  Generating scaling functions and wavelets from filter coefficients

Unit 5 Bi-orthogonal Wavelets

6 lecture hours

 Bi-orthogonal Wavelet bases  Filtering relationship for Bi-orthogonal filters  Bi-orthogonal scaling functions and wavelets  Two dimensional wavelets  Non separable Multi-dimensional wavelets  Wavelet Packets

Unit 6 Wavelength Transform and applications

8 lecture hours

 Transform coding  DTWT for image compression
audio compression  Wavelet based audio coding
video coding and multi resolution Techniques  Wavelet de-noising
Speckle removal
Edge detection and object isolation  Image fusion
Object detection
discrete wavelet multi-tone modulation

Unit 7 Beyond Wavelet

4 lecture hours

 Ridge lets and curve lets: Ridge let transform and Digital Curve let transform  Curve let construction  Properties and applications

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Wavelet Transforms and Applications

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Wavelet Transforms and Applications Syllabus — Unit-wise Content

Unit 1 Introduction

Unit 2 Continuous Wavelet Transform

Unit 3 Introduction to the Discrete Wavelet Transform and orthogonal Wavelet decomposition

Unit 4 MRA Ortho-normal wavelets and their relationships to filter banks

Unit 5 Bi-orthogonal Wavelets

Unit 6 Wavelength Transform and applications

Unit 7 Beyond Wavelet

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