# Motivation for Wavelets and Some Simple Examples

## Abstract

In the first part of the book the focus was on approximating functions or vectors with trigonometric counterparts. We saw that Fourier series and the Discrete Fourier transform could be used to obtain such approximations, and that the FFT provided an efficient algorithm. This approach was useful for analyzing and filtering data, but had some limitations. Firstly, the frequency content is fixed over time in a trigonometric representation. This is in contrast to most sound, where the characteristics change over time. Secondly, we have seen that even if a sound has a simple trigonometric representation on two different time intervals, the representation as a whole may not be simple. In particular this is the case if the function is nonzero only on a very small time interval.

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