ABSTRACT
The Fourier transform plays a very important role in a multitude of scientific and engineering fields. This chapter describes the concept of the Fourier series and its extension, and introduces the Fourier transform. It discusses an important concept in system analysis, that is, the convolution integral, the correlation function and their Fourier transforms. Convolution and correlation are very important concepts in some scientific and engineering areas. The chapter introduces the sampling theorem to transform analog signals into digital signals. The normalized and orthogonal polynomials are called the normalized orthogonal polynomials. The Fourier transform of a convolution integral gives us the product of Fourier transforms of each function. To consider applications of Fourier transform, we introduce a function corresponding to an impulse. The chapter also describes that Fourier series can be interpreted as expansion of a periodic function into sinusoidal functions.
