Jf. Chicharo et Mt. Kilani, ARBITRARY MULTIFREQUENCY ESTIMATION AND THE RELATIONSHIP BETWEEN THE LMS AND GOERTZEL ALGORITHMS, International journal of electronics, 83(3), 1997, pp. 287-298
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.