Wavelets: Multi-Resolution Signal Processing

Abstract

Fourier Transform has been considered to be a well accepted transformation both for time domain and spatial signal analysis since late 1950s. A relatively new transformation technique named as wavelet transform has been utilized even in a better way for 1D and 2D signal decomposition, compression, encoding and different methods of analysis and synthesis. Conventional Fourier Transform lags of the localized analysis of signal in terms of frequency content. Discrete Wavelet Transform (DWT) refers to a class of transformations that differ not only in the transformation kernel employed but also in the fundamental nature of the basis functions and in the way in which they are applied. A set of scaled and shifted wavelet basis can be used to to represent any kind of signal in a time-frequency or space-frequency localized manner. The last section of this chapter deals with an application of the DWT to image compression. We have formally introduced and described the technique of Embedded Zero-tree Wavelet (EZW) coding for image compression based on levels of significance according to bit-budget.