The mel-frequency-cepstrum is a representation of a signal's spectral envelope warped onto the mel scale, a perceptual frequency scale where equal distances sound equally spaced to human ears. It is computed by: (1) applying a windowed Fourier transform (STFT) to obtain the power spectrum; (2) mapping the spectrum frequencies to the mel scale using triangular overlapping windows; (3) taking the logarithm of the mel-spectrum energies; (4) applying a discrete cosine transform to produce the cepstral coefficients. The mel-warped representation captures the timbral structure of speech and audio more faithfully than linear-frequency cepstra for human-centered applications. [formal: mfc | substrate: mind | horizon: hours | explicit: yes | epoch: 1.00]
Accepted ontology entry
mel-frequency-cepstrum
The mel-frequency-cepstrum is a representation of a signal's spectral envelope warped onto the mel scale, a perceptual frequency scale where equal distances sound equally spaced to human ears. It is computed by: (1) applying a windowed Fou…
Definition
Why it is in scope
A frequency representation of a signal obtained by mapping the spectrum onto a non-linear mel-scale and computing the cepstrum — used in speech recognition, audio classification, and speaker identification as a perceptually-motivated feature extraction method.
Names and aliases
- mel-frequency-cepstrumen · CANONICAL
Relations from this entry
- cmsqhjrqb000lti676a6qcrwrINSTANCE_OF →
Mel-frequency-cepstrum IS a specific kind of cepstral-coefficients representation — it is a cepstral representation obtained via mel-warped spectrum. Law 9: a competent speaker would call MFC 'a cepstral coefficient set'.
- cmspjfefp05lxjlssg1w6gyuvDEPENDS_ON →
MFC is computed by taking a cepstrum of a mel-warped spectrum. Remove the cepstrum operation and MFC cannot exist — it is the core computational step of MFC. The removal test (Law 8) passes.
- cmspwlkct06sxjlsset2q9og2DEPENDS_ON →
MFC maps the spectrum onto the mel-scale before computing the cepstrum. The mel-scale warping is essential — remove it and MFC collapses to ordinary cepstrum. The removal test passes (Law 8).
- cmsqg4mko005f3e32eyp15c4sDEPENDS_ON →
MFC computation requires STFT as the foundation — the mel-filterbank operates on the STFT magnitude spectrum. Remove STFT and MFC has no input to warp. The removal test passes.
- cmsqhjrqb000lti676a6qcrwrDERIVED_FROM →
MFCCs were developed after cepstral-coefficients (1980s vs 1970s) and build on them by adding a mel-scale filterbank. Cepstral-coefficients existed first and fed into MFCCs. Which-came-first test: cepstral-coefficients predates MFCC. Law 7.
- cmsrkc1pl01pskp531dangmpeDEPENDS_ON →
Mel-frequency cepstrum is computed from a mel-frequency-spectrum via DCT. The spectrum is the direct input to the cepstral computation. Remove mel-frequency-spectrum and the cepstrum has no source data. Law 8 removal test passes.
- cmsrkc1pl01pskp531dangmpeDERIVED_FROM →
The mel-frequency cepstrum is derived from the mel-frequency spectrum via DCT. Which-came-first: the spectrum concept predates and feeds into the cepstrum computation. The spectrum is the input; the cepstrum is the derived output.
- cmspjfefp05lxjlssg1w6gyuvINSTANCE_OF →
mel-frequency-cepstrum is a specific kind of cepstrum, using the mel-scale filterbank instead of an octave-scale. A competent speaker would call it 'a cepstrum'.
- cmspxgu9f06vtjlssp8aaz07zDEPENDS_ON →
The mel-frequency cepstrum requires the mel filterbank to transform the log-magnitude spectrum into mel-scaled bins. Remove the mel filterbank and the mel-frequency cepstrum cannot operate — the filterbank is the mechanism that creates the mel-scale spectral representation which the cepstrum then DCT-transforms. Removal test: no filterbank → no mel-frequency cepstrum.
- cmspjfefp05lxjlssg1w6gyuvDERIVED_FROM →
Mel-frequency-cepstrum DERIVED_FROM cepstrum — the mel-frequency variant applies the mel scale to the cepstrum computation. The cepstrum concept (the 'pectrum domain via inverse FFT of log spectrum) existed first and general; mel-frequency-cepstrum is a specific warping of that older concept. Which-came-first: cepstrum (epoch ~0.05) predates mel-frequency-cepstrum (epoch ~0.08).
Relations to this entry
- cmspw3d3806pzjlss3rcmuezg← INSTANCE_OF
MFCC (Mel-Frequency Cepstral Coefficients) is a specific instance of mel-frequency-cepstrum: it computes cepstral coefficients from the mel-frequency spectrum via DCT, specifically the log-magnitude variant. A competent speaker would call MFCC 'a mel-frequency cepstrum'.
Record identity
- Created
- Aug 13, 2026, 11:39 AM UTC
- Content hash
- e66e4436dcbdeb925be19f6303f7c3be02e8df99c8e367c3e09b46f582f3a951