ABSTRACT
W. Kenneth Jenkins
Alexander D. Poularikas
Bruce W. Bomar
L. Montgomery Smith
James A. Cadzow
Dean J. Krusienski
The Fourier transform is a mathematical tool that is used to expand signals into a spectrum of sinusoidal
components to facilitate signal representation and the analysis of system performance. In certain applications
the Fourier transform is used for spectral analysis, while in others it is used for spectrum shaping that adjusts
the relative contributions of different frequency components in the filtered result. In certain applications the
Fourier transform is used for its ability to decompose the input signal into uncorrelated components, so that
signal processing can be more effectively implemented on the individual spectral components. Different forms
of the Fourier transform, such as the continuous-time Fourier series, the continuous-time Fourier transform,
the discrete-time Fourier transform (DTFT), the discrete Fourier Transform (DFT), and the fast Fourier
transform are applicable in different circumstances. One goal of this section is to clearly define the various
Fourier transforms, to discuss their properties, and to illustrate how each form is related to the others in the
context of a family tree of Fourier signal processing methods.
