ABSTRACT
Anyone working in engineering or the physical sciences will know some of the transformations named in this chapter’s title. Laplace and Fourier transforms are much used in electric circuit theory, electromagnetic theory (including optics), and signal processing. The Z transformation has in the past two generations proved a major tool in the field of digital signal processing, while the Hilbert transform is useful in subjects as diverse as the modulation of radio signals as well as the analysis of brain waves. Because of the similarity of Laplace and Fourier transforms, we treat them first and begin with the easier of the two, Laplace.
