DISCRETE AND INTEGRAL FOURIER-TRANSFORMS - ANALYTICAL EXAMPLES

Analytical examples of the discrete Fourier transform (DFT) help in un derstanding relations between the DFT and the Fourier integral transfo rm (FIT). Such examples enable one to estimate the errors involved whe n one transform is approximated by the other, and they suggest how suc h approximation errors might be reduced. We present mathematical and n umerical analyses of the time-to-frequency DFT of the complex exponent ial function and of the frequency-to-time inverse DFT of the relaxatio n function. The FITs of these functions are exact inverses, and so the y serve to clarify the effects of aliasing and truncation on the DFT.