Approximations to Fourier Transforms
Roger L. Easton · 2010
This chapter considers two methods for approximating spectra if the Fourier integral has no known closed-form solution. Though the expressions are valid over limited regions of the frequency domain, they are useful in certain situations and also may help the reader develop intuition about the behavior of the Fourier transform of some other more complicated functions. The first approximation is a series expansion for F[?] in powers of ?. The second approximate form of the Fourier transform obtained by the “method of stationary phase” may be evaluated only for functions that satisfy some specific criteria and is valid only for large values of |?|. The developments of these two approximations in this chapter are followed by the introduction of the so-called “central-limit theorem”, which may provide an approximate expression for the action of a multistage imaging system. Controlled Vocabulary Terms Fourier transforms