THE WAVELET TRANSFORM

THE WAVELET TRANSFORM

FUNDAMENTAL CONCEPTS & OVERVIEW

TRANSFORM

Why do we need a Transform?
Mathematical transformations are applied to signals to obtain further information from that signal that is not readily available in the raw signal. Most of the signals in practice are time-domain signals in their raw format. That is, whatever that signal is measuring, is a function of time. When we plot time-domain signals, we obtain a time-amplitude representation of the signal. This representation is not always the best representation of the signal for most signal processing related applications. In many cases, the most distinguished information is hidden in the frequency content of the signal. The frequency spectrum of a signal is basically the frequency components (spectral components) of that signal. The frequency spectrum of a signal shows what frequencies exist in the signal. To examine frequency content of the signal, we need to transform signal from time-domain to frequency domain.

Various Transformation Techniques
There a There are number of transformations that can be applied, among which the Fourier transforms (FT) are probably by far the most popular. If the FT of a signal in time domain is taken, the frequency-amplitude representation of that signal is obtained. There are many other transforms that are used quite often by engineers and mathematicians. Hilbert transform, short-time Fourier transform, Wigner distributions, the Radon Transform, and of course, the Wavelet transform, constitute only a small portion of a huge list of transforms that are available at engineer's and mathematician's disposal. Every transformation technique has its own area of application, with advantages and disadvantages, and the wavelet transform (WT) is no exception.


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