Simplified six-point discrete Fourier transforms

Five different algorithms were developed to implement a six-point discrete Fourier transform (DFT) method. The DFT was then used to calculate a related quantity,. the power spectral density (PSD). A recursive implementation of a time domain Banning window was derived to minimize side-lobe leakage.

Five algorithms were implemented on a computer. Timing studies and verification of results were performed on synthetically generated data. A sixth program was written for actual data analysis using one of the five algorithms.

The six-point DFT was designed to reduce the number of multiplications required in the calculation and thus reduce the execution time required for computer computation of the DFT. Results show comparable speed to presently used fast Fourier transform (FFT) tehniques. However some of the new algorithms developed yield results on a logarithmic frequency separation which may be found more useful in certain applications. Practical application of the agorithms developed was demonstrated by analyzing noise data from a nuclear power plant.