### 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