A cepstrum-coefficient is the individual amplitude value obtained at a specific quefrency from the cepstrum computation: the inverse Fourier transform of the logarithm of a signal's power spectrum. Each coefficient corresponds to one quefrency point and encodes periodic structure in the signal's spectrum — low quefrency coefficients capture broad spectral shape, high quefrency coefficients resolve fine spectral detail. The construct persists through standard notation (e.g., c[n] or Cep(n)), mathematical tables, and practical applications in speech recognition (MFCCs), fault diagnosis, and audio analysis. [formal: coefficient | substrate: mind | horizon: hours | explicit: yes | epoch: 0.01]
Accepted ontology entry
cepstrum-coefficient
A cepstrum-coefficient is the individual amplitude value obtained at a specific quefrency from the cepstrum computation: the inverse Fourier transform of the logarithm of a signal's power spectrum. Each coefficient corresponds to one quefr…
Definition
Why it is in scope
A human-made mathematical construct: the individual values obtained as output of the cepstrum computation — the amplitude of the inverse Fourier transform of the log-power spectrum, each indexed by quefrency. Built to persist through notation in signal processing, audio analysis, and diagnostic engineering, where cepstral coefficients serve as feature representations for classification and pattern detection.
Names and aliases
- cepstrum-coefficienten · CANONICAL
Relations from this entry
- cmspsgnup06f0jlssh5w4odx3DERIVED_FROM →
The cepstrum-coefficient is computed via the inverse DFT of the log-power spectrum: c[n] = IDFT(log(|X[k]|²)). The DFT concept (1820s) predates cepstral coefficients (1963, Bogert). Which-came-first test passes: DFT existed first and fed into cepstrum-coefficient.
- cmrwraj00012csoaclnxvq1ekDERIVED_FROM →
The cepstrum-coefficient is computed as IDFT(log(|X[k]|²)). The logarithm concept (1600s, Napier/Bregg) predates cepstrum-coefficients (1963, Bogert). Logarithm is used as the mathematical machinery in the computation. Which-came-first test passes.
- cmspg0fzk056ijlss3ydafq7bSERVES →
Cepstrum-coefficients are computed (c[n]=IDFT(log|X[k]|²)) specifically to enable spectral analysis of signals — their designed purpose is to further spectral-analysis as a diagnostic technique in fault detection, speech processing, and engineering. The coefficients serve the analysis, not the other way around.
- cmsps9i0v06eejlssqrjcqyviSERVES →
Cepstrum-coefficients are computed specifically to serve signal-processing: they are features extracted from signals for pattern recognition within signal-processing pipelines (speech recognition, fault detection). For whose sake? The coefficients point at signal-processing as their master domain.
- cmspcwtqk04tkjlsslitlqy58DEPENDS_ON →
Cepstrum-coefficients are computed from the power spectrum (c[n]=IDFT(log|X[k]|²)). Remove the power-spectrum concept and cepstrum-coefficients cannot be computed — the removal test passes as present-tense operational necessity.
- cmspjfefp05lxjlssg1w6gyuvDERIVED_FROM →
The cepstrum (the function/operation) existed first and fed into the cepstrum-coefficient (the numerical values extracted from it). Which came first: the cepstrum concept, or its coefficients? The cepstrum came first — coefficients are derived values from the cepstrum function.
- cmspmjaky05vwjlss1p9r2wo0INSTANCE_OF →
A cepstrum coefficient is a specific kind of cepstral coefficient — it is the numerical value at a specific quefrency point in a cepstrum. Cepstral coefficient is the general category of coefficients in any cepstral representation; cepstrum coefficient refers specifically to values in the quefrency-domain cepstrum.
Relations to this entry
- cmspjfefp05lxjlssg1w6gyuv← CONTAINS
The cepstrum is the sequence of cepstrum-coefficients indexed by quefrency. Each cepstrum-coefficient is a constituent part — the cepstrum IS the collection of these values, making this a whole-part relation.
- cmspw3d3806pzjlss3rcmuezg← DERIVED_FROM
MFCC builds on the cepstrum-coefficient concept: it computes coefficients in the cepstral domain (log power spectrum via DCT). Cepstrum-coefficient as a mathematical concept existed before MFCC was devised. Which came first? cepstrum-coefficient. Valid DERIVED_FROM (Law 7).
- cmsqals7w0004ox1y79lqk3dy← DERIVED_FROM
Cepstral-envelope is derived from cepstrum-coefficients: it is obtained by smoothing/filtering the cepstral coefficients to extract the slowly-varying envelope shape, discarding the fine-structure (residual) components.
Record identity
- Created
- Aug 12, 2026, 8:16 AM UTC
- Content hash
- 0e5985d8e675f20c1adf0aac8a87413ccda97886c3e05c223671d33664de1764