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.
Faculty Advisor Name
Susan E. Kelly
Faculty Advisor Institution
University of Wisconsin - La Crosse
Suggested Mathematics Subject Classification(s)
42C40, 42A16
Recommended Citation
Nicholas G. Roland, Fourier and Wavelet Representations of Functions, Furman University Electronic Journal of Undergraduate Mathematics, 6 (2016), 1-12. Available at: https://scholarexchange.furman.edu/fuejum/vol6/iss1/1
Comments
This paper was written while the author was an undergraduate student at the University of Wisconsin - La Crosse. The paper is also published in the University of Wisconsin - La Crosse Journal of Undergraduate Research.