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.[1] 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:[2][3]

  1. Take the Fourier transform of (a windowed excerpt of) a signal.
  2. Map the powers of the spectrum obtained above onto the mel scale, using triangular overlapping windows or alternatively, cosine overlapping windows.
  3. Take the logs of the powers at each of the mel frequencies.
  4. Take the discrete cosine transform of the list of mel log powers, as if it were a signal.
  5. 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,[4] or addition of dynamics features such as "delta" and "delta-delta" (first- and second-order frame-to-frame difference) coefficients.[5]

The European Telecommunications Standards Institute in the early 2000s defined a standardised MFCC algorithm to be used in mobile phones.[6]

  1. ^ Min Xu; et al. (2004). "HMM-based audio keyword generation" (PDF). In Kiyoharu Aizawa; Yuichi Nakamura; Shin'ichi Satoh (eds.). Advances in Multimedia Information Processing – PCM 2004: 5th Pacific Rim Conference on Multimedia. Springer. ISBN 978-3-540-23985-7. Archived from the original (PDF) on 2007-05-10.
  2. ^ Sahidullah, Md.; Saha, Goutam (May 2012). "Design, analysis and experimental evaluation of block based transformation in MFCC computation for speaker recognition". Speech Communication. 54 (4): 543–565. doi:10.1016/j.specom.2011.11.004. S2CID 14985832.
  3. ^ Abdulsatar, Assim Ara; Davydov, V V; Yushkova, V V; Glinushkin, A P; Rud, V Yu (2019-12-01). "Age and gender recognition from speech signals". Journal of Physics: Conference Series. 1410 (1): 012073. Bibcode:2019JPhCS1410a2073A. doi:10.1088/1742-6596/1410/1/012073. ISSN 1742-6588. S2CID 213065622.
  4. ^ Fang Zheng, Guoliang Zhang and Zhanjiang Song (2001), "Comparison of Different Implementations of MFCC," J. Computer Science & Technology, 16(6): 582–589.
  5. ^ S. Furui (1986), "Speaker-independent isolated word recognition based on emphasized spectral dynamics"
  6. ^ European Telecommunications Standards Institute (2003), Speech Processing, Transmission and Quality Aspects (STQ); Distributed speech recognition; Front-end feature extraction algorithm; Compression algorithms. Technical standard ES 201 108, v1.1.3.