ARBITRARY MULTIFREQUENCY ESTIMATION AND THE RELATIONSHIP BETWEEN THE LMS AND GOERTZEL ALGORITHMS

The relationship between the LMS and the sliding Goertzel (SG) algorit hms for Fourier coefficient estimation of sinusoidal components is des cribed given a priori information of the input frequencies. This relat ionship is established from the point of view that both methods may be considered as narrow bandpass filters tuned to the exact input freque ncy locations. The LMS algorithm is equivalent to an infinite impulse response (IIR) filter bank which has similar parametrization as the re sonator-based filter bank proposed by Padmanabhan and Martin (1987). I t is also shown that the SG algorithm provides significant computation al 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 consid ered.