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.Bridle and Brown used a set of 19 weighted spectrum-shape coefficients given by the cosine transform of the outputs of a set of nonuniformly spaced bandpass filters. The filter spacing is chosen to be logarithmic above 1 kHz and the filter bandwidths are increased there as well. We will, therefore, call these the mel-based cepstral parameters. 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 cepstrum. This frequency warping can allow for better representation of sound, for example, in audio compression. MFCCs are commonly derived as follows: 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. MFCC values are not very robust in the presence of additive noise, and so it is common to normalise their values in speech recognition systems to lessen the influence of noise. Some researchers propose modifications to the basic MFCC algorithm to improve robustness, such as by raising the log-mel-amplitudes to a suitable power (around 2 or 3) before taking the DCT (Discrete Cosine Transform), which reduces the influence of low-energy components. Paul Mermelstein is typically credited with the development of the MFC. Mermelstein credits Bridle and Brown for the idea: