JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

Prerequisite

None

Course Objectives

• 1. To learn basics of two-dimensional transform.
• 2. Understand the various two-dimensional transform definition, properties and applications.
• 3. Understand the design of filter Bank structure.
• 4. To learn the fundamentals of wavelet transform and special wavelets.

Course Outcomes

On completion of this course student will be able to:

• 1. The student will learn basics of two-dimensional transforms.
• 2. Understand the definition, properties and applications of various two-dimensional transform.
• 3. Understand the basic concepts of wavelet transform.
• 4. Understand the special topics such as wavelet packets, Bi-orthogonal wavelets e.t.c.

UNIT - I

Fourier Analysis: Vector space, Hilbert spaces, Fourier basis, FT- Limitations of Fourier Analysis, Need for time-frequency analysis, DFT, 2D-DFT: Definition, Properties and Applications, IDFT, Hilbert Transform, STFT.

UNIT - II

Transforms: Walsh, Hadamard, Haar and Slant Transforms, DCT, DST, KLT– Definition, Properties and applications.

UNIT - III

Continuous Wavelet Transform (CWT): Short comings of STFT, Need for wavelets, Wavelet Basis- Concept of Scale and its relation with frequency, Continuous time wavelet Transform Equation- Series Expansion using Wavelets, CWT, Tiling of time scale plane for CWT, Important Wavelets: Haar, Mexican Hat, Meyer, Shannon, Daubechies.

UNIT - IV

Multi Rate Analysis and DWT: Need for Scaling function, Multi Resolution Analysis, Two-Channel Filter Banks, Perfect Reconstruction Condition, Relationship between Filter Banks and Wavelet Basis, DWT, Structure of DWT Filter Banks, Daubechies Wavelet Function, Applications of DWT.

UNIT - V

Special Topics: Wavelet Packet Transform, Multidimensional Wavelets, Bi-orthogonal basis- B- Splines, Lifting Scheme of Wavelet Generation, Multi Wavelets.

TEXT BOOKS

• 1. Wavelet Transforms-Introduction theory and applications -Raghuveer M. Rao and Ajit S. Bopardikar, Pearson Edu, Asia, New Delhi, 2003.
• 2. “Insight into Wavelets from Theory to practice “, Soman. K. P, Ramachandran. K.I, Prentice Hall India, First Edition, 2004. R19 M.TECH EIE

REFERENCES:

• 1. “Fundamentals of Wavelets- Theory, Algorithms and Applications”, Jaideva C Goswami, Andrew K Chan, John Wiley & Sons, Inc, Singapore, 1999.
• 2. “Wavelets and sub-band coding”, Vetterli M. Kovacevic, PJI, 1995.
• 3. “Introduction to Wavelets and Wavelet Transforms”, C. Sydney Burrus, PHI, First Edition, 1997.
• 4. “A Wavelet Tour of Signal Processing”, Stephen G. Mallat, Academic Press, Second Edition, 2008. R19 M.TECH EIE M.TECH.- I YEAR- I SEMESTER ELECTRONICS AND INSTRUMENTATION ENGINEERING