Abstract
The relationship between the LMS and the sliding Goertzel (SG) algorithms for Fourier coefficient estimation of sinusoidal components is described given a priori information of the input frequencies. This relationship is established from the point of view that both methods may be considered as narrow bandpass filters tuned to the exact input frequency locations. The LMS algorithm is equivalent to an infinite impulse response (IIR) filter bank which has similar parametrization as the resonator-based filter bank proposed by Padmanabhan and Martin (1987). It is also shown that the SG algorithm provides significant computational savings when compared to the LMS algorithm under the same accuracy and acquisition time conditions. For illustration purposes the problem of dual tone multifrequency (DTMF) estimation and detection is considered.
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