Cepstrum analysis - Cut off frequencies displayed

1. What is cepstrum analysis in vibration?
2. How do you calculate cepstrum?
3. What is cepstral analysis of speech?
4. Why is cepstrum used?

What is cepstrum analysis in vibration?

Cepstrum Analysis is a tool for the detection of periodicity in a frequency spectrum, and seems so far to have been used mainly in speech analysis for voice pitch determination and related questions.

How do you calculate cepstrum?

The real cepstrum of a signal x, sometimes called simply the cepstrum, is calculated by determining the natural logarithm of magnitude of the Fourier transform of x, then obtaining the inverse Fourier transform of the resulting sequence: c x = 1 2 π ∫ - π π log | X ( e j ω ) | e j ω n d ω .

What is cepstral analysis of speech?

The Cepstral Analysis is a tool for detecting periodicity in the frequency spectrum and it is mainly used in pitch detection, radar and sonar applications, speech analysis, and diagnostics.

Why is cepstrum used?

The cepstrum had been used in speech analysis for determining voice pitch (by accurately measuring the harmonic spacing), but also for separating the formants (transfer function of the vocal tract) from voiced and unvoiced sources, and this led quite early to similar applications in mechanics.