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.

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