<title>Artificial neural networks and Abelian harmonic analysis</title>

This work deals with the use of artificial neural networks (ANN) for the digital processing of finite discrete time signals. The effort concentrates on the efficient replacement of fast Fourier transform (FFT) algorithms with ANN algorithms in certain engineering and scientific applications. The FFT algorithms are efficient methods of computing the discrete Fourier transform (DFT). The ubiquitous DFT is utilized in almost every digital signal processing application where harmonic analysis information is needed. Applications abound in areas such as audio acoustics, geophysics, biomedicine, telecommunications, astrophysics, etc. To identify more efficient methods to obtain a desired spectral information will result in a reduction in the computational effort required to implement these applications.