Practical Signals Theory with MATLAB Applications, 2nd Edition

Chapter 8The Laplace Transform

The Fourier transform has been studied as a way to represent a signal as a linear decomposition of orthogonal sinusoidal components. By transforming a time domain signal to the frequency domain as , calculations are often simpler, and the new perspective of a different domain can give a better understanding of signals behavior. In many applications, another 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, the Laplace transform adds an exponential dimension to the frequency domain and calls this the s-domain. Consequently, the Laplace transform of a time domain signal is the complex function having both frequency and exponential components. The s-domain function describes a ...