A log-magnitude-spectrum is the base-10 logarithmic transformation of a magnitude spectrum, computed as 10·log₁₀(|X(f)|²) where X(f) is the frequency-domain representation of a signal segment. It converts multiplicative convolution in the time domain (e.g. source-filter separation in speech) into additive decomposition, enabling linear modeling of spectral envelope. The transformation is implemented as a mathematical operation within DSP pipelines and audio analysis software. [formal: log-magnitudo-spectrum | substrate: mind | horizon: a moment | explicit: yes | epoch: 0.01]
Accepted ontology entry
log-magnitude-spectrum
A log-magnitude-spectrum is the base-10 logarithmic transformation of a magnitude spectrum, computed as 10·log₁₀(|X(f)|²) where X(f) is the frequency-domain representation of a signal segment. It converts multiplicative convolution in the…
Definition
Why it is in scope
A human-made spectral representation computed by taking the base-10 logarithm of the magnitude spectrum — a perceptually-motivated transformation used in audio analysis, speech processing, and music information retrieval that converts multiplicative signal structures into additive ones.
Names and aliases
- log-magnitude-spectrumen · CANONICAL
Relations from this entry
- cmspqj6jh0677jlssnhgl6v8dDERIVED_FROM →
Log-magnitude-spectrum is derived from magnitude-spectrum by applying a log transformation. Which existed first? magnitude-spectrum predates and feeds into log-magnitude-spectrum. The which-came-first test passes.
- cmsq4obya07m0jlssh92wv3v0INSTANCE_OF →
Log-magnitude-spectrum is a specific kind of spectral representation obtained by applying a logarithmic transform to spectral magnitudes. A competent speaker calls it a type of spectral representation. Specific→general per Law 9. Nearest kind is spectral-representation (Law 11e).
- cmspqj6jh0677jlssnhgl6v8dDEPENDS_ON →
Log-magnitude-spectrum is computed by applying a logarithmic transform to magnitude-spectrum values. Remove magnitude-spectrum as a concept and the input for the log transform disappears — the operation stops. Real operational dependency (Law 8b).
- cmspdibrl04whjlssto99iiufDERIVED_FROM →
Which came first? The Fourier transform (1822) predates and feeds into the log-magnitude spectrum. The log-magnitude spectrum is computed by taking the Fourier transform of a signal, extracting the magnitude, then taking the log. Fourier transform is the historical and computational predecessor.
- cmsqglbgv00763e32jisx8hz3INSTANCE_OF →
Log-magnitude-spectrum is a specific kind of spectral feature — it represents spectral energy in logarithmic scale across frequency bins. A competent speaker would call a log-magnitude spectrum a spectral feature. Nearest kind.
Relations to this entry
- cmsqhjrqb000lti676a6qcrwr← DEPENDS_ON
Cepstral coefficients are computed as IFFT of the log-magnitude-spectrum. Remove the log-magnitude-spectrum concept and cepstral coefficient computation stops — the removal test passes. The log-magnitude is an operational prerequisite in the cepstral pipeline.
- cmspw3d3806pzjlss3rcmuezg← DERIVED_FROM
log-magnitude spectrum predates mfcc: MFCC computation takes the log-magnitude spectrum as intermediate input after STFT and before the mel filterbank. Older concept feeds into newer.
- cmsqhjrqb000lti676a6qcrwr← DERIVED_FROM
Which-came-first test: log-magnitude spectrum (post-Fourier, 19th century) predates cepstral coefficients (1960s, Bolger). Cepstral coefficients are computed from the log-magnitude spectrum: take log of magnitude spectrum, then apply inverse FFT. The log-magnitude spectrum is the direct input.
Record identity
- Created
- Aug 13, 2026, 1:29 PM UTC
- Content hash
- f86acf055e019f43a626a31521a706a3385619431b8615f7838f8739c170405d