Mel-frequency cepstrum

In sound processing, the mel-frequency cepstrum (MFC) is a representation of the short-term power spectrum of a sound, based on a linear cosine transform of a log power spectrum on a nonlinear mel scale of frequency. Mel-frequency cepstral coefficients (MFCCs) are coefficients that collectively make up an MFC. They are derived from a type of cepstral representation of the audio clip (a nonlinear "spectrum-of-a-spectrum"). The difference between the cepstrum and the mel-frequency cepstrum is that in the MFC, the frequency bands are equally spaced on the mel scale, which approximates the human auditory system's response more closely than the linearly-spaced frequency bands used in the normal spectrum. This frequency warping can allow for better representation of sound, for example, in audio compression that might potentially reduce the transmission bandwidth and the storage requirements of audio signals. MFCCs are commonly derived as follows: Take the Fourier transform of (a windowed excerpt of) a signal. Map the powers of the spectrum obtained above onto the mel scale, using triangular overlapping windows or alternatively, cosine overlapping windows. Take the logs of the powers at each of the mel frequencies. Take the discrete cosine transform of the list of mel log powers, as if it were a signal. The MFCCs are the amplitudes of the resulting spectrum. There can be variations on this process, for example: differences in the shape or spacing of the windows used to map the scale, or addition of dynamics features such as "delta" and "delta-delta" (first- and second-order frame-to-frame difference) coefficients. The European Telecommunications Standards Institute in the early 2000s defined a standardised MFCC algorithm to be used in mobile phones. MFCCs are commonly used as features in speech recognition systems, such as the systems which can automatically recognize numbers spoken into a telephone. MFCCs are also increasingly finding uses in music information retrieval applications such as genre classification, audio similarity measures, etc.