In this chapter we introduce several transforms that are commonly used in engineering applications. Except for the Laplace transform, which can be used in a variety of applications, the other integral transforms are considered more specialized. We also briefly discuss the notion of a discrete Fourier transform, a discrete Laplace transform (called the Z-transform), and a discrete Walsh transform.
Integral transforms are common working tools of every engineer and scientist. The Fourier transform studied in Chapter 9 is basic to frequency spectrum analysis of time-varying waveforms. Here, we study the Laplace transform used in control theory and in the analysis of initial-value problems like those associated with electric circuits. In addition, we introduce the Hankel transform (directly related to a two-dimensional Fourier transform) and the Mellin transform. The Hankel transform is essential to the analysis of diffraction theory and image formation in optics (see ), and the Mellin transform is useful in probability theory and in optical wave propagation (see ).
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