The Haar Discrete Wavelet Transform

Summary

In contrast to Fourier analysis, there exist an infinite number of discrete wavelet transform (DWT) basis signals. While most of these types of signals cannot be defined by analytical expressions, the Haar basis signals are exceptions. This chapter primarily presents the Haar DWT in terms of transform matrices. It provides formulas and examples of transform matrices for various data lengths and levels of decomposition. The chapter explores the row‐column method of computing the 2‐D Haar DWT. It discusses application of the DWT for the detection of discontinuities in signals. The time‐frequency resolutions of the DWT, with N = 8, are also shown. While the DWT analysis can be carried out using the filter coefficients without any knowledge of the corresponding continuous basis functions, it is good to look at them for a better understanding of the transform.