melspectrum

A melspectrum, or mel spectrum, is a spectral representation in which the spectral energy of an audio signal is mapped onto the mel scale using a mel-filterbank. The mel scale is a perceptual scale of pitches that more closely matches human auditory perception, with finer resolution at low frequencies and coarser resolution at higher frequencies.

To compute a melspectrum, an audio signal is typically divided into short frames, a window (such as a Hamming window) is applied, and a Fourier transform yields the magnitude or power spectrum for each frame. A mel filterbank, consisting of overlapping triangular filters spaced along the mel scale, is then applied to the spectrum. The energy (or power) in each filter is summed to produce a vector of mel energies for that frame. Often the logarithm of these energies is taken to obtain the log-mel spectrum. The result can be represented per frame or stacked across frames as a time-frequency feature.

The mel spectrum is designed to emulate the auditory processing of the human ear and is widely used as a lower-dimensional, perceptually informed alternative to the full Fourier spectrum. It reduces spectral resolution at higher frequencies and emphasizes components that are more perceptually relevant for speech and audio analysis.

Relation to other concepts: applying a discrete cosine transform (DCT) to the log-mel spectrum yields mel-frequency cepstral coefficients (MFCCs), a compact feature widely used in speech recognition and related tasks. The mel spectrum itself is commonly used in speech and music information retrieval, often as a preprocessing step before classification or similarity analysis. Typical choices include 40 mel bands, frame lengths of 20–40 ms, and hop sizes of 10–20 ms, with common sampling rates being 16 kHz or 44.1 kHz.