Introduction to Laplace space and the Laplace transform
Patrick A. Gaydecki · Institution of Engineering and Technology eBooks · 2004
Both the Laplace transform and the z-transform are closely related to, respectively, the continuous Fourier transform and the discrete time Fourier transform. However, because they employ a complex frequency variable (s or z) rather than a purely imaginary one (jω), they are more general in scope. The Laplace transform is for example, ubiquitously employed for the analysis and design of electrical circuits such as filters and networks, and is ideally suited for the analysis of transient response phenomena (Hickmann, 1999). Similarly the z-transform is an indispensable tool for the design and analysis of digital filters, especially infinite impulse response (ΠR) filters, of which we will have much to say in this and later chapters.