Accurate FFT differentiation techniques

Date

1983

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Abstract

The Fast Fourier Transform (FFT) is an efficient algorithm to compute the discrete Fourier transform. The objective of this thesis is to analyze a variety of problems which lead to inaccurate results in standard FFT differentiation techniques. Methods vdiich inprove computational accuracy are also reviewed. Two main approaches are followed in order to inprove the accuracy of the estimated derivative. The Fourier coefficients of the function are estimated more accurately in the first approach. The second approach is to inprove the convergence of the Fourier series of the function. The methods discussed are tested using FFT routines available on the FPS 100 array processor. The results indicate that the latter approach leads to a higher accuracy.

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Keywords

Fourier transformations, Fourier analysis

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