Recursive discrete Fourier transformation

This paper presents new discrete Fourier transform methods which are recursive, expressible in state variable form, and which involve real number computations. The algorithms are especially useful for running Fourier transformation and for general and multirate sampling. Numerical examples are given which illustrate the ability of these spectral observers to operate at sampling rates other than the Nyquist rate, to perform one-step-per-sample updating, and to converge to the spectrum in the presence of severe numerical truncation error.