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 practiceô€€€,
Prentice Hall, 2004.
No comments:
Post a Comment