mel-frequency-spectrum

Mel-frequency spectrum is computed by mapping the magnitude spectrum onto the mel scale. Remove the magnitude spectrum concept and mel-frequency spectrum computation collapses — there is nothing to map. Removal test passes (Law 8b). The log-magnitude variant similarly depends on magnitude-spectrum.

Mel-frequency-spectrum is a specific kind of time-frequency representation that maps spectral content onto the mel perceptual scale. A competent speaker calls it a time-frequency method. Specific→general per Law 9. The nearest kind is time-frequency-representation, not spectral-representation (Law 11e).

The mel-frequency spectrum maps spectral content onto the mel scale — a perceptual frequency scale. Removal test: remove mel-scale as a concept and the mel-frequency spectrum has no frequency axis to map onto; its entire purpose (perceptual frequency warping) disappears. Constitutive dependency.

Mel-frequency spectrum is computed by first obtaining the STFT magnitude spectrum, then warping it to the mel scale. Removal test: remove stft and there is no spectral representation to warp. Constitutive dependency.

Mel-frequency spectrum is a specific kind of spectral representation that maps the frequency axis onto a perceptual mel scale. A competent speaker would call MFCC 'a spectral representation.' Files against nearest accepted kind.

The mel-frequency spectrum is derived from the general spectrum concept: it applies a mel-scale frequency warping to the linear frequency spectrum. The mel scale existed as a perceptual model after the spectrum concept, and the mel-frequency spectrum as a concept is obtained by transforming the spectrum through the mel-scale filterbank. Which existed first? The linear spectrum concept predates the mel-warping transformation.

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.

A mel-frequency-spectrum IS a specific kind of spectral-feature — it represents spectral content mapped to the mel-frequency scale. A competent speaker would call it 'a type of spectral feature.' Files against nearest kind (Law 9).

MFCC (Mel-frequency cepstral coefficients) is computed from a mel-frequency-spectrum. It takes the mel-frequency spectrum as its input and applies a DCT to its log-magnitude values. Remove mel-frequency-spectrum as the input concept and MFCC has no data to process — the technique stops operating. Law 8 removal test passes.

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.

MFCC is derived from the mel-frequency spectrum through DCT transformation. The spectrum existed first and served as the raw material from which MFCC coefficients are computed. Which-came-first: mel-frequency-spectrum predates MFCC and feeds into it.

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.

Chroma features are computed by folding mel-frequency-spectrum data into pitch-class bins. Remove mel-frequency-spectrum and chroma has no spectral input to fold — it stops operating. Removal test (Law 8) passes.