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Applied Mathematical Methods by Bhaskar Dasgupta

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42

Fourier Transforms

In Chap. 36, we studied an integral transform, namely the Laplace transform. Here, drawing from the Fourier integral in the previous chapter, we work out our second integral transform, the Fourier transform, and study its properties. Subsequently, we briefly discuss the topic of the discrete Fourier transform, which has great application in the technology of signal processing.

Definition and Fundamental Properties

In a notational departure from the previous chapter, we will mostly denote a function as f (t) here, rather than f (x). Quite often, we will also treat the independent variable t with the notion of ‘time’. The reader should, however, bear in mind that Fourier transforms are defined with respect to other variables ...

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