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The Computer Journal 1969 12(2):160-164; doi:10.1093/comjnl/12.2.160
© 1969 by British Computer Society
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An error analysis of Goertzel's (Watt's) method for computing Fourier coefficients

W. M. Gentleman *

Bell Telephone Laboratories Incoporated, Murray Hill, New Jersey, USA

Goertzel's method, also known as Watt's algorithm, is one of the three standard methods of computing Fourier coefficients, and is especially commonly used when only a small number of coefficients is desired for a given sequence. This paper gives a floating-point error analysis of the technique, and shows why it should be avoided, particularly for low frequencies.

Received November 1967. revised November 1968.

* Bell Telephone Laboratories, Incorporated, Murray Hill, New Jersey (Temporarily at Division of Numerical and Applied Mathematics, National Physical Laboratory, Teddington, Middlesex.)


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