# Properties of Fourier Cosine and Sine Transforms

### Abstract

The time and frequency domains are alternative ways of representing signals. The Fourier transform is the mathematical relationship between these two representations. These transformations are of interest mainly as tools for solving ODEs, PDEs and integral equations, and they often also help in handling and applying special functions [8,9]. In this article, I have outlined the main features of properties of Fourier cosine and sine Transforms. These properties demand the implementation of representation of a function in integral form, known as Fourier cosine and sine transforms. The purpose of this paper is to provide a brief representation any function in integral form, Fourier cosine and sine transforms, after multiplying the given function by power functions;### References

Remarks on history of abstract harmonic analysis, Radomir S. Stankovic, Staakko T. Astola1, Mark G. Karpovsky2

James S. Walker, University of Wisconsin-Eau clarie

Linear Partial Differential Equations for Scientists and Engineers, Tyn Myint-U Lokenath Debnath, 2007

Differential Equation and Integral Equations, Peter J. Collins, 2006.

Differential Equations, James R. Brannan, William E. Boyce, 2nd edition.

Advanced Engineering Mathematics 7th Edition, PETER V. ONEIL.

Historically, how and why was the Laplace Transform invented? Written 18 Oct 2015 From Wikipedia:

The frequency domain Introduction: http://www.netnam.vn/unescocourse/computervision/91.htm.

JPNM Physics Fourier Transform:

http://www.med.harvard.edu/JPNM/physics/didactics/improc/intro/fourier2.html.

*International Journal of Sciences: Basic and Applied Research (IJSBAR)*,

*35*(3), 184-193. Retrieved from https://www.gssrr.org/index.php/JournalOfBasicAndApplied/article/view/7910

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