MFCCs

MFCCs, or mel-frequency cepstral coefficients, are a widely used feature representation in speech and audio processing. They capture the spectral envelope of a sound by mapping the power spectrum onto a perceptually motivated mel scale and then decorrelating the result with a discrete cosine transform.

The computation of MFCCs typically involves several steps. The audio signal is pre-emphasized and divided into short frames, usually 20–40 milliseconds in length with overlap. Each frame is windowed, commonly with a Hamming window, and the power spectrum is estimated via the Fourier transform. The spectrum is passed through a bank of triangular filters spaced on the mel scale, and the energies of these filters are summed. These log energies approximate human loudness perception. A discrete cosine transform is then applied to the log energies to produce the cepstral coefficients. In practice, 12–13 coefficients are commonly retained per frame, with the 0th coefficient sometimes omitted or replaced by the frame’s log energy.

Extensions and variants include adding delta and delta-delta (temporal derivative) features to capture dynamics, and applying normalization or alternative perceptual scales. Robustness can be enhanced with techniques such as cepstral mean and variance normalization (CMVN).

MFCCs are standard inputs for automatic speech recognition, speaker identification, and many audio classification tasks. They offer compact, interpretable representations of spectral shape but can be sensitive to noise, channel effects, and frame parameters, and may be complemented by other features in noisy environments.