DS4072 Wavelet Transforms and Applications Syllabus:
DS4072 Wavelet Transforms and Applications Syllabus – Anna University PG Syllabus Regulation 2021
COURSE OBJECTIVES:
To study the basics of signal representation and Fourier theory
To understand Multi Resolution Analysis and Wavelet concepts
To study the wavelet transform in both continuous and discrete domain
To understand the design of wavelets using Lifting scheme
To understand the applications of Wavelet transform
UNIT I FUNDAMENTALS
Vector Spaces – Properties– Dot Product – Basis – Dimension, Orthogonality and Orthonormality – Relationship Between Vectors and Signals – Signal Spaces – Concept of Convergence – Hilbert Spaces for Energy Signals- Fourier Theory: Fourier series expansion, Fourier transform, Short time Fourier transform, Time-frequency analysis
UNIT II MULTI RESOLUTION ANALYSIS
Definition of Multi Resolution Analysis (MRA) – Haar Basis – Construction of General Orthonormal MRA – Wavelet Basis for MRA – Continuous Time MRA Interpretation for the DTWT – Discrete Time MRA – Basis Functions for the DTWT – PRQMF Filter Banks.
UNIT III CONTINUOUS WAVELET TRANSFORMS
Wavelet Transform – Definition and Properties – Concept of Scale and its Relation with Frequency – Continuous Wavelet Transform (CWT) – Scaling Function and Wavelet Functions(Daubechies Coiflet, Mexican Hat, Sinc, Gaussian, Bi Orthogonal)– Tiling of Time – Scale Plane for CWT
UNIT IV DISCRETE WAVELET TRANSFORM
Filter Bank and Sub Band Coding Principles – Wavelet Filters – Inverse DWT Computation by Filter Banks – Basic Properties of Filter Coefficients – Choice of Wavelet Function Coefficients –Derivations of Daubechies Wavelets – Mallat’s Algorithm for DWT –Multi Band Wavelet Transforms Lifting Scheme- Wavelet Transform Using Polyphase Matrix actorization – Geometrical Foundations of Lifting Scheme – Lifting Scheme in Z –Domain.
UNIT V APPLICATIONS
Wavelet methods for signal processing- Adaptive wavelet techniques in signal acquisition, Detection of signal changes, analysis and classification of audio signals using CWT, Signal and Image compression Techniques: EZW–SPIHT Coding– Image Denoising Techniques: Noise Estimation – Shrinkage Rules – Shrinkage Functions –Edge Detection and Object Isolation, Image Fusion, and Object Detection. Wavelet based signal de-noising and energy compaction, Wavelets in adaptive filtering, Digital Communication and Multicarrier Modulation, Trans multiplexers.
COURSE OUTCOMES:
CO1:Use Fourier tools to analyse signals
CO2:Gain knowledge about MRA and representation using wavelet bases
CO3:Acquire knowledge about various wavelet transforms and design wavelet transform
CO4:Apply wavelet transform for various signal &communication applications
CO5:Apply wavelet transform for various image processing applications
TOTAL:45 PERIODS
REFERENCES:
1. Rao R M and A S Bopardikar, ―Wavelet Transforms Introduction to theory and Applications, Pearson Education, Asia, 2012.
2. L.PrasadS.S.Iyengar, Wavelet Analysis with Applications to Image Processing, CRCPress, 1997.
3. J. C. Goswami and A. K. Chan, Fundamentals of wavelets: Theory, Algorithms and Applications, WileyIntersciencePublication,John Wiley & Sons Inc., 2011.
4. M. Vetterli, J. Kovacevic, Wavelets and subband coding, Prentice Hall Inc, 2013.
5. Stephen G. Mallat, A wavelet tour of signal processing, 2 nd Edition Academic Press,2009.
6. Soman K P and Ramachandran K I, Insight into Wavelets From Theory to practice, Prentice Hall, 2010.