By the end of this chapter, the reader will be able to:
The Fourier transform has been studied as a way to represent a signal s(t) as a linear decomposition of orthogonal sinusoidal components. By transforming a time-domain signal s(t), calculations are often simpler, and the new perspective of a different domain can give a better understanding of signals behavior. In many applications, a different transform technique is required, one that goes beyond sinusoidal components and incorporates the ability to manipulate the derivative and integral response functions that are typically found in real systems. The Laplace transform is sometimes described as a general-purpose Fourier transform, although the two transforms usually serve in different applications.
While the Fourier transform relates the time and frequency domains, ...