Why transforms?

In the field of signal processing we frequently encounter the use of transforms . Transforms are named such because they take a signal and transform it into another signal, hopefully one which is easier to process oranalyze than the original. Essentially, transforms are used to manipulate signals such that their most importantcharacteristics are made plainly evident. To isolate a signal's important characteristics, however, one must employ atransform that is well matched to that signal. For example, the Fourier transform, while well matched to certain classesof signal, does not efficiently extract information about signals in other classes. This latter fact motivates ourdevelopment of the wavelet transform.