DOI link for Fourier Transforms
Fourier Transforms book
The Fourier transform is certainly one of the best known of the integral transforms and vies with the Laplace transform as being the most generally useful. Since its introduction by Fourier in the early 1800s, it has found use in innumerable applications and has, itself,
led to the development of other transforms. Today the Fourier transform is a fundamental tool in engineering science. Its importance has been enhanced by the development in the twentieth century of generalizations extending the set of functions that can be Fourier transformed and by the development of efﬁcient algorithms for computing the discrete version of the Fourier transform.