Implementation of the Discrete Wavelet Transform
D. Sundararajan · 2015
The discrete wavelet transform (DWT) is essentially a set of bandpass filters and their efficient implementation. In this chapter, the implementation of the DWT using typical filters is described. There are two approaches to implement the DWT. The first approach is to evaluate the required convolutions directly. The other approach is to factorize the polyphase matrix into a product of a set of sparse matrices. Signal decomposition, downsampling, upsampling, and reconstruction constitute the essential multirate digital signal processing operations required for the implementation of the DWT. The Haar filters constitute a two-band uniform DFT filter bank, and the implementation is similar to that of the DFT using fast algorithms. The DWT coefficients are computed by convolving the filter coefficients with the input data. The chapter also considers the implementation of the DWT using the Daubechies orthogonal filter of length 4. Symmetrical filters provide an effective solution to the boundary problem.