Capstrum analysis

  It is obtained by inverse Fourier transforming of the power spectrum (logarithmically transformed) obtained by Fourier transforming the signal. Its horizontal axis is called keffrency, and its unit is time (ms in this application). The frequency (Hz) is obtained as the inverse of the cephrency of the peak observed in the cepstrum. Applying this method to vocal sounds, we can determine the pitch (= vibration frequency of the vocal cords) of the voice.
  Fourier transforming this cepstrum with all but the low cephrency part of the cepstrum set to 0 yields the approximate shape of the spectrum (spectral envelope). This spectral envelope represents the resonance characteristics of the vocal tract in vocal sounds and is considered an important factor in voice identification.

  In this application, when the Waveform button is tapped twice on the analysis screen, it becomes the FFT analysis button, and the Spectrum button appears to the right of it. Press it twice and it becomes the Cepstrum button and the results of the cepstrum analysis are displayed.
  The black line graph is the cepstrum, and the reciprocal of the time of its peak gives the fundamental frequency.
  The red line graph shows the spectral envelope calculated by the method described above. In this envelope graph, a tap on the left or right side of the screen changes the frequency range, and a tap on the top or bottom part moves the graph position up or down.
The figure below shows the "i" sound, with a fundamental frequency of 123 Hz, which represents the frequency of the vocal folds. The first formant is approximately 350 Hz, and the second formant is approximately 2600 Hz.