A mel-frequency cepstral coefficient is a sample of a [[mel-frequency cepstrum]]. Its computation takes the following steps: 1. Compute the [[discrete Fourier transform (DFT)]] of the signal $ X(k)=\sum_{n=0}^{N-1} x(n) e^{-j\frac{2\pi}{N}kn},\;0 \leq k \leq N-1 $ 2. Compute the [[mel-frequency spectrum]]: $ M(r) = \frac{1}{A_{r}} \sum_{k=L_{r}}^{U_{r}} |V_{r}(k) X(k)| $ where $V_{r}(k)$ is the triangular weighting function for the 𝑟-th filter, $L_{r}$ and $U_{r}$ are the lower and upper indices of the frequencies of the triangular filter, $A_r$ is the amplitude normalization factor of the filter. This groups the DFT values in critical bands. 3. Compute the [[discrete cosine transform (DCT)]] of the logarithm of the magnitude of the filter outputs: $ MFCC(m) = \frac{1}{R} \sum_{r=1}^{R} \ln(M(r)) \cos\left( \frac{\pi}{R}\left( r + \frac{1}{2} \right)m \right) $ where $R$ is the number of mel filters. The number of MFCC coefficients is typically less than the number of mel filters.