A Review of Repetition Rate as Fundamental Frequency Extraction in Complex Voice Signals

Fundamental frequency is difficult to determine from visual observation of a spectrogram or waveform when the lowest component is weak, or subharmonics are present. The purpose of this study was to test fundamental frequency extraction algorithms under these conditions.

The greatest common divisor (GCD) between harmonic components was used to define the fundamental frequency. Waveforms were produced with sinusoidal components of various amplitudes and phases. State-of-the-art algorithms were used to extract the fundamental frequency from a composite waveform when the lowest sinusoid was weak, nonexistent, or confounded with a subharmonic.

The majority of algorithms predicted GCD as the f_o, even when only two harmonically related sinusoids were present, and the fundamental was missing. However, the lowest frequency of a period-2 subharmonic was predicted as the fundamental frequency when its amplitude was above 30% of the amplitude of the lowest harmonic.

Fundamental frequency extraction of complex speech waveforms in speech or song needs more careful consideration when signals are complex. Future work should include the presence of period-3 and period-4 subharmonics, as well as sideband and difference frequencies. Perceptual experiments should be conducted to correlate the GCD predictions with auditory perception.