# Overview

This analyser conducts cepstral analysis for each window of the audio file. A real cepstrum is the inverse Fourier transform of the logarithm of the magnitude of a Fourier transform. As such, it is similar to auto-correlation analysis, and can be used to pitch analysis and echo detection. Cepstral analysis is widely used in voice analysis because it provides a simple way to separate formants (due to filtering in the vocal tract) from the vocal source.

The real cepstrum may give better results than the complex cepstrum if results are being viewed in the cepstrum domain.

Output is given as a function of ‘quefrency’, which is very similar to the lag time of auto-correlation. The output level is ‘gamnitude’ (given in dB of dB). Calibration is not particularly meaningful because of the non-linear nature of the transformation, but the same calibration offset as the FFT Spectrum analyser is used. Note that gamnitude is not complex, with positive and negative values, so an alternative would be to avoid the dB transformation – the disadvantage of this being the large range of values in typical analyses.

The real cepstrum analyser is implemented using Matlab’s rceps(x) operator.

# User Controls

## Overlap

This sets the overlap of windows in terms of percentage, milliseconds, seconds or number of samples.

## Window Size

This sets the size of the window in samples, which is a power of 2. Values from 2^7 (128 samples) to 2^20 (1048576 samples) are supported (corresponding to window durations of 2.9 ms to 23.8 s for a sampling rate of 44.1 kHz). Longer window durations could be achieved by downsampling the waveform prior to analysis.

A larger window size increases the frequency resolution, but reduces the time resolution. A larger window size is computationally more efficient, but requires greater memory. A non-rectangular windowing function could be thought of as reducing the effective window length.

## Windowing Function

This selects the windowing function to be applied to the wave prior to the analysis. Windowing functions provide a ‘fade-in’ and ‘fade-out’ of the windowed waveform, which is helpful in the analysis of arbitrary waves. Select the rectangular window for no effect.

# Outputs

## Cepstrogram

This is the magnitude of the cepstrum (expressed in decibels) as a function of quefrency and time. The actual units are decibels of decibels.

*Example of a cepstrogram of a solo operatic tenor. Large values of quefrency correspond to low fundamental frequencies*

## Average Power Cepstrum

This is the power average (over time) of the cepstra as a function of frequency, expressed in decibels. In some cases this will return no data because at least one of the windows in the analysis yielded an invalid result.

## Cepstral Moments

Standardized and non-standardized moments spectral of the power cepstrum are given as time series.

# Verification

No verification yet.

# Code Authors

This analyser was written by the PsySound3 team.

# Key References

Digital signal processing and spectral analysis books often have information on cepstral analysis. For example:

Oppenheim, A.V., and R.W. Schafer. Discrete-Time Signal Processing. Englewood Cliffs, NJ: Prentice Hall, 1989