FAST FOURIER TRANSFORM ALGORITHM.

An explanation is given of the Discrete Fourier Transform in terms of its action on real pulse and sinusoidal data. Even real data is seen to give rise to even real spectra, and odd real data produces odd imaginary spectra. The idea of aliases, leakage and windows are examined. The Fast Fourier Transform is a method of performing the DFT and it is approached firstly by decimation in time and then by decimation in frequency. The terms twiddle factor, bit reversal, shuffling, butterflies and radix are introduced. Application of the FFT in correlation, convolution, band limited interpolation and coherence functions is discussed. The Chirp Z Transform performed by convolution in a transversal filter is examined, as it seems to be the cheapest and fastest method of performing the DFT.