An error analysis of Goertzel's (Watt's) method for computing Fourier coefficients

Abstract

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.