Limitations of standard Fourier analysis. Windowed Fourier transform. Continuous wavelet transform. Time-frequency resolution.
Wavelet bases. Balian-Low theorem. Multiresolution analysis. (MRA). Construction of wavelets from MRA. Fast wavelet algorithm.
Compactly supported wavelets. Cascade algorithm. Franklin and spline wavelets. Wavelet packets.Hilbert space frames. Frame representation. Representation of signals by frames. Iterative reconstruction. Frame algorithm.
Wavelet methods for signal processing. Noise suppression. Representation of noise-corrupted signals using frames. Algorithm for reconstruction from corrupted frame representation.
Wavelet methods for image processing. Burt- Adelson and Mallat’s pyramidal decomposition schemes. 2D- dyadic wavelet transform.
1. E.Hernandez & G.Weiss, A First Course on Wavelets, CRC Press, 1996.
2. L.Prasad & S.S.Iyengar, Wavelet Analysis with Applications to Image Processing, CRC Press, 1997.
1. A.Teolis, Computational Signal Processing with Wavelets, Birkhauser, 1998
2. R.M. Rao & A.S. Bopardikar, Wavelet Transforms, Addition Wesley, 1998.
3. J.C. Goswami & A.K. Chan, Fundamentals of Wavelets, John Wiley,1999.
Students are able to
CO1: understand about windowed Fourier transform and difference between windowed Fourier transform and wavelet transform.
CO2: understand wavelet basis and characterize continuous and discrete wavelet transforms
CO3: understand multi resolution analysis and identify various wavelets and evaluate their time- frequency resolution properties
CO4: implement discrete wavelet transforms with multirate digital filters
CO5: understand about wavelet packets
CO6: design certain classes of wavelets to specification and justify the basis of the application of wavelet transforms to different fields
