of Microprocessors

588 MUSICAL ApPLICATIONS OF MICROPROCESSORS
corresponds to the fundamental frequency of the sound. The reciprocal of the
quefrency of the peak is the fundamental frequency. This peak will be present
even if the actual fundamental and several lower harmonics of the analyzed
tone are missing, a situation that confuses pitch detectors using low-pass
preprocessing.
However, confusion is possible in certain cases. For example, if the
excitation function has only odd order harmonics such as a square or triangular
wave, the cepstrum will give a fundamental frequency twice its correct
value. This is because the cepstrum essentially responds to periodicity of
harmonic spacing, and the spacing of odd order harmonics is twice the fundamental
frequency. A pure sine wave, which all other schemes discussed
handle beautifully, gives a pitch estimate equal to the reciprocal of the record
length used in analysis! These failures could be a problem with certain kinds
of musical instrument sound such as a clarinet or a flute. Thus, cepstral pitch
detection should be augmented by other pitch-detection schemes for
maximum accuracy.