ABSTRACT
The wavelet transform can be viewed as yet another way to describe the properties of a waveform that changes over time, but in this case, the waveform is divided not into sections of time, but segments of scale. The wavelet transform introduces an intriguing twist to the basic concept of a sliding correlation. In wavelet analysis, a basis of family members is also used, but the family members consist of enlarged or compressed versions of the base function. Designing the filters to be used in a wavelet filter bank can be quite challenging because the filters must meet a number of criteria. Wavelet analysis based on filter bank decomposition is particularly useful for detecting small discontinuities in a waveform. Wavelet analysis includes two quite different approaches: the CWT and the DWT. The wavelet family is constructed from a base waveform, called the “mother wavelet,” that is then stretched or compressed in time to make up the various family members.
