Cepstrum

Part of speech: noun

Definitions

1. A spectrum-of-a-spectrum used in signal processing to separate periodic structure, such as pitch in speech, from the overall spectral envelope
2. The result of taking the logarithm of a signal's power spectrum and then transforming it back, which reveals regularly spaced harmonics in audio analysis
3. A quefrency-domain representation produced by applying an inverse Fourier transform to the log magnitude spectrum of a time series or sound

Etymology: The most striking thing about "cepstrum" is that it was built by deliberately scrambling a familiar word. Take "spectrum," reverse its first syllable, and you get "cepstrum," a joke that the statisticians who coined it appear to have made on purpose. The term describes a spectrum taken of a spectrum: you compute the spectrum of a signal, take the logarithm of it, and then analyse that result again. The reversal was a deliberate wink at the way the method works. The procedure turns the original signal's frequency information into a new domain, sometimes called the quefrency domain, where the names of familiar quantities are also scrambled. Frequency becomes "quefrency," and the filter becomes a "liftering" operation, so the whole vocabulary plays with the same joke. The result is a tool for separating two kinds of structure that overlap in an ordinary spectrum. Periodic features such as the pitch of a voice show up as a distinct peak, which can be separated from the slower-changing spectral envelope that shapes vowels. That separation is why the technique became central to speech recognition.