CU7006 WAVELET TRANSFORMS AND APPLICATIONS-ANNA UNIV PG 1ST SEM SYLLABUS

ANNA UNIVERSITY, CHENNAI

REGULATIONS - 2013

M.E. APPLIED ELECTRONICS

CU7006 WAVELET TRANSFORMS AND APPLICATIONS

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
Factorization – Geometrical Foundations of Lifting Scheme – Lifting Scheme in Z –Domain.

UNIT V APPLICATIONS
Wavelet methods for signal processing- Image Compression Techniques: EZW–SPHIT Coding– Image Denoising Techniques: Noise Estimation – Shrinkage Rules – Shrinkage Functions –Edge Detection and Object Isolation, Image Fusion, and Object Detection.

TOTAL: 45 PERIODS 

COURSE OUTCOMES:
Upon Completion of the course, the students will be able to
 Use Fourier tools to analyse signals
 Gain knowledge about MRA and representation using wavelet bases
 Acquire knowledge about various wavelet transforms and design wavelet transform
 Apply wavelet transform for various signal & image processing applications
TEXT BOOKS:
1. Rao R M and A S Bopardikar, ―Wavelet Transforms Introduction to theory and
Applications, Pearson Education, Asia, 2000.
2. L.Prasad & S.S.Iyengar, Wavelet Analysis with Applications to Image Processing, CRC
Press, 1997.

REFERENCES:
1. J. C. Goswami and A. K. Chan, “Fundamentals of wavelets: Theory, Algorithms and
Applications" WileyInterscience Publication,John Wiley & Sons Inc., 1999.
2. M. Vetterli, J. Kovacevic, “Wavelets and subband coding" Prentice Hall Inc, 1995.
3. Stephen G. Mallat, “A wavelet tour of signal processing" 2 nd Edition Academic Press,
2000.
4. Soman K P and Ramachandran K I, ―Insight into Wavelets From Theory to practice􀀀,
Prentice Hall, 2004.