of Microprocessors

SOURCE-SIGNAL ANALYSIS 587
Quite obviously, eithet method involves a lot of calculation, approximately
M X N operations, where M is the number of samples in the
waveform section being analyzed and N is the number of lags tried in the
peak/dip search. It can be reduced substantially by only evaluating lags that
are close to the last measured pitch period.
In theory, true autocorrelation is guaranteed to produce maximumheight
peaks only at multiples of the true period. Thus, any perfectly
periodic waveform will be correctly analyzed by the autocorrelation method.
A changing waveform, however, is a different story. When the waveform
changes, the peak corresponding to the pitch period is smaller than it would
otherwise be because of the inexact repetition. There ate also additional peaks
that may be due to strong harmonics, formants, etc. If the pitch peak
attenuation due to waveform change is great enough, these secondary peaks
will cause an error.
Frequency-Domain Methods
Pitch detection in the frequency domain is fairly simple to understand
but does imply a lot of computation to obtain the spectrum. However, if the
spectrum is used for formant analysis, then the additional processing necessary
for pitch detection is relatively minor.
The most straightforward frequency-domain pitch-detection scheme is
an extension of frequency analysis mentioned earliet. The idea is to take the
measured frequency of each significant component found and determine the
greatest common divisor. For example, if components were found at 500 Hz,
700 Hz, 1,100 Hz, and 1,500 Hz, the fundamental would be 100 Hz
because it is the highest possible frequency for which all of the measured
frequencies are harmonics. In real life, though, the frequency measurements
will not be exact because of noise, a changing spectrum, etc. Thus, classic
greatest-common-divisor algorithms will have to be extensively modified to
allow some slop. Also, confining attention to the strongest half-dozen or
fewer components will lessen the likelihood of confusion. If the least common
multiple turns out to be a ridiculous number such as 20 Hz (any value
less than the spectrum analysis bandwidth is suspect), then an unpitched
sound should be assumed.
The primary difficulty with the frequency-analysis method is the restriction
on harmonic spacing so that accutate analysis is assured. When low
fundamental frequencies are to be analyzed, this leads to very long analysis
records and the possibility of significant frequency content changes over the
duration of the record, which in turn can lead to errors.
Homomorphic spectral analysis leads to a very good pitch detector, in
fact one of the best available for speech sounds. In a cepstral plot, the
low-quefrency values correspond to the spectrum shape, while highquefrency
values correspond to the excitation function. For harmonic-rich
tones, there will be a single sharp peak in the upper part of the cepstrum that