mel-filterbank

Mel-filterbank (1980s, newer) derives from mel-scale (Stevens et al. 1937, older). The filterbank is built by applying triangular windows spaced according to the mel scale. Which-came-first: mel-scale predates mel-filterbank by decades.

The mel filterbank is a specific kind of filter (a bank of triangular bandpass filters spaced on the mel perceptual scale) used in signal processing. A competent speaker would describe it as 'a filter'. Direction is specific→general (Law 9). Filter is the nearest accepted kind.

The mel filterbank is deliberately designed and maintained for spectral analysis — it shapes the frequency response to match human perception, enabling spectral feature extraction. Law 8d: for whose sake? Spectral analysis.

The mel filterbank is a deliberate component of the MFCC computation pipeline — it shapes frequency response into mel-scaled bands before cepstral coefficient extraction. MFCC as a whole is designed to consume the mel filterbank's output. Law 8d: for whose sake? MFCC.

Mel-filterbank applies triangular filters on a perceptually-warped frequency axis. Without freq-warping, it operates on a linear axis and does not produce the perceptually-scaled mel features that define it. The removal test: remove freq-warping and mel-filterbank stops operating as mel-filterbank.

Mel-filterbank operates on a spectral representation as its input data. Remove spectral-representation (the frequency-domain data structure) and the mel-filterbank has no data to filter — the removal test passes. The triangular weighting is applied to spectral bins.

Mel-filterbank computation needs signal processing — FFT to get the magnitude spectrum, and spectral analysis to apply the mel-spaced triangular filters. Remove signal processing and mel-filterbank cannot operate.

The mel-filterbank concept DERIVED_FROM spectrum: it takes the spectral representation as its input and organizes frequency bins along the mel scale. Spectrum existed first as the frequency-domain representation, and the mel-filterbank was built on top of it as a perceptual weighting mechanism.

Mel-filterbank is designed and maintained for the sake of MIR — it maps spectra to the mel scale to produce perceptually-relevant spectral representations (mel-spectrograms) that are the standard input for MIR systems. The designed purpose is to further MIR's operation. Law 8d: servant→master.

A mel filterbank IS a specific kind of filter bank — a bank of triangular bandpass filters spaced along the mel frequency scale. A competent speaker would call it 'a filter bank.' Files against the nearest established kind per Law 9/11e. (My previous rejection was for INSTANCE_OF spectral-feature, which was a category error — a filterbank is a mechanism, not a spectral feature.)

The mel-frequency filterbank is defined entirely by the mel frequency scale — its bands are spaced according to the mel scale. Remove the mel scale and the filterbank has no purpose or definition. Constitutive present-tense dependency.

A mel filterbank maps frequency bins to mel-scale bins using triangular filters centered at specific frequencies. Remove frequency and the filterbank has no domain to operate on — it literally maps between frequency representations. Genuine DEPENDS_ON.

A mel filterbank implements a set of bandpass filters spaced according to the mel-frequency scale; the filterbank design is historically and conceptually downstream of the scale definition.

A mel-filterbank is a bank of overlapping bandpass filters spaced on the mel scale. Remove filters as an operation and the mel-filterbank has no mechanism — it IS a collection of filter operations. The removal test passes: without filters, a mel-filterbank cannot function.

The mel filterbank is parameterized by the mel-frequency scale; removing the scale removes the filterbank's defining spacing and center frequencies. The filterbank depends on the scale for its operation.

MFCC computation applies a mel-scale filterbank to the FFT output as a necessary step — remove the mel-filterbank and MFCC cannot produce mel-scaled representations. Present-tense operational dependency per Law 8.

The mel-scale filterbank was developed first as a model of human auditory frequency resolution (Byrne and Greenberg, 1981). The mel-spectrum is computed by applying this pre-existing filterbank to a power spectrum. Which-came-first test: filterbank concept predates mel-spectrum as a named construct.

Mel-spectrum is the power spectrum transformed by the mel-filterbank. Remove the mel-filterbank concept and mel-spectrum has no operational definition — it is nothing without the filterbank. Present-tense DEPENDS_ON per Law 8.

MFCC computation derives from mel-filterbank: the mel-scale filterbank extracts band energies from the spectrum, which is the foundational step before the DCT produces cepstral coefficients. The mel-scale frequency warping (originating from mel-filterbank research) is integral to the MFCC derivation.

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.

mel-frequency-spectrum is computed by applying a mel filterbank to the magnitude spectrum. Remove the mel filterbank and the mel-frequency-spectrum cannot be computed — the filterbank is the operational mechanism.

Chroma feature extraction operates by applying a mel-scale filterbank to the magnitude spectrum, then folding into pitch classes. The mel filterbank is the constitutive mechanism — remove it and chroma features cannot be computed as defined. Present-tense removal test passes.

A mel-spectrogram is computed by applying a mel filterbank to a power spectrogram. Remove the mel filterbank and the mel-spectrogram cannot be produced — it stops operating as a mel-spectrogram. Per Law 8 removal test.

MFCC computation applies mel filterbank to magnitude spectrum then takes DCT; removing mel filterbank stops MFCC from operating.

MCD is computed from mel-cepstral coefficients derived via mel-filterbank analysis of the spectrum. Remove mel-filterbank and the cepstral coefficients cannot be formed, so MCD stops operating.