Discrete Wavelet Transform

Abstract

According to the definition of the continuous wavelet transform (CWT) given in (3.7), Chap. 3, the scale parameter s and translation parameter $\tau$ can be varied continuously. As a result, performing the CWT on a signal will lead to the generation of redundant information. Although the redundancy is useful in some applications, such as signal denoising and feature extraction where desired performance is achieved at the cost of increased computational time and memory size, other applications may need to emphasize reduced computational time and data size, for example, in image compression and numerical computation. Such requirements illustrate the need for reducing redundancy in the wavelet coefficients among different scales as much as possible, while at the same time, avoiding sacrificing the information contained in the original signal. This can be achieved by parameter discretization, as described in the following section.