Volume 6, 2000. 1 - 12. 
Nicholas G. Roland
Fourier and Wavelet Representations of Functions

Abstract. Representations of functions are compared using the traditional technique of Fourier series with a more modern technique using wavelets. Under certain conditions, a function can be represented with a sum of sine and cosine functions. Such a representation is called a Fourier series. This classical method is used in applications such as storage of sound waves and visual images on a computer. One problem with this sum is that it is infinite. In use, only a finite number of terms can be used. More accuracy requires more terms in the series, but more terms require more time to compute and more space to store. A new type of sum called a wavelet series was first introduced in the 1980's. With these new series the same accuracy often takes fewer terms. Since wavelet representations can be more accurate and take less computer time, they are often more useful.

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Furman University Electronic Journal of Undergraduate Mathematics