mgcep
Functions
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int main(int argc, char *argv[])
mgcep [ option ] [ infile ]
-m int
order of coefficients \((0 \le M)\)
-a double
all-pass constant \((|\alpha| < 1)\)
-g double
gamma \((|\gamma| \le 1)\)
-c int
gamma \(\gamma = -1 / C\) \((1 \le C)\)
-l int
FFT length \((2 \le N)\)
-q int
input format
0amplitude spectrum in dB1log amplitude spectrum2amplitude spectrum3power spectrum4windowed waveform
-o int
output format
0mel-cepstrum1MLSA filter coefficients2gain normalized mel-cepstrum3gain normalized MLSA filter coefficients.
-i int
number of iterations \((0 \le J)\)
-d double
convergence threshold \((0 \le \epsilon)\)
-e double
small value added to power spectrum
-E double
relative floor in decibels
infile str
double-type windowed sequence or spectrum
stdout
double-type mel-generalized cepstral coefficients
In the example below, mel-cepstral coefficients are extracted from
data.d.frame < data.d | window | mgcep > data.mcep
This is equivalents to the below line.
frame < data.d | window | fftr -o 3 -H | mgcep -q 3 > data.mcep
- Parameters:
argc – [in] Number of arguments.
argv – [in] Argument vector.
- Returns:
0 on success, 1 on failure.
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class MelCepstralAnalysis
Calculate mel-cepstrum from periodogram.
The input is the half of periodogram:
\[ \begin{array}{cccc} |X(0)|^2, & |X(1)|^2, & \ldots, & |X(N/2)|^2, \end{array} \]where \(N\) is the FFT length. The output is the \(M\)-th order mel-cepstral coefficients:\[ \begin{array}{cccc} \tilde{c}(0), & \tilde{c}(1), & \ldots, & \tilde{c}(M). \end{array} \]In the mel-cepstral analysis, the spectrum of speech signal is modeled by \(M\)-th order mel-cepstral coefficients as follows:
\[ H(z) = \exp \sum_{m=0}^M \tilde{c}(m) \tilde{z}^{-m}, \]where\[ \tilde{z}^{-1} = \frac{z^{-1} - \alpha}{1 - \alpha z^{-1}} \]is first order all-pass function. The phase characteristic of the all-pass function is controlled by \(\alpha\). The typical values that approximate the mel-scale are summarized below.Sample rate [kHz]
Alpha
8
0.31
10
0.35
12
0.37
16
0.42
22.05
0.45
32
0.50
44.1
0.53
48
0.55
Note that the implemenation is based on an unpublished paper.
Public Functions
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MelCepstralAnalysis(int fft_length, int num_order, double alpha, int num_iteration, double convergence_threshold)
- Parameters:
fft_length – [in] Number of FFT bins, \(N\).
num_order – [in] Order of cepstral coefficients, \(M\).
alpha – [in] All-pass constant, \(\alpha\).
num_iteration – [in] Number of iterations of Newton method, \(J\).
convergence_threshold – [in] Convergence threshold, \(\epsilon\).
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inline int GetFftLength() const
- Returns:
FFT length.
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inline int GetNumOrder() const
- Returns:
Order of coefficients.
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inline double GetAlpha() const
- Returns:
All-pass constant.
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inline int GetNumIteration() const
- Returns:
Number of iterations.
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inline double GetConvergenceThreshold() const
- Returns:
Convergence threshold.
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inline bool IsValid() const
- Returns:
True if this object is valid.
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bool Run(const std::vector<double> &periodogram, std::vector<double> *mel_cepstrum, MelCepstralAnalysis::Buffer *buffer) const
- Parameters:
periodogram – [in] \((N/2+1)\)-length periodogram.
mel_cepstrum – [out] \(M\)-th order mel-cepstral coefficients.
buffer – [out] Buffer.
- Returns:
True on success, false on failure.
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class Buffer
Buffer for MelCepstralAnalysis class.
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MelCepstralAnalysis(int fft_length, int num_order, double alpha, int num_iteration, double convergence_threshold)
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class MelGeneralizedCepstralAnalysis
Calculate mel-generalized cepstrum from periodogram.
The input is the half of periodogram:
\[ \begin{array}{cccc} |X(0)|^2, & |X(1)|^2, & \ldots, & |X(N/2)|^2, \end{array} \]where \(N\) is the FFT length. The output is the \(M\)-th order mel-generalized cepstral coefficients:\[ \begin{array}{cccc} \tilde{c}_\gamma(0), & \tilde{c}_\gamma(1), & \ldots, & \tilde{c}_\gamma(M). \end{array} \]In the mel-generalized cepstral analysis, the spectrum of speech signal is modeled by \(M\)-th order mel-generalized cepstral coefficients as follows:
\[\begin{split}\begin{eqnarray} H(z) &=& s^{-1}_\gamma \left( \sum_{m=0}^M \tilde{c}_\gamma(m) \tilde{z}^{-m} \right) \\ &=& \left\{ \begin{array}{ll} \left( 1 + \gamma \displaystyle\sum_{m=0}^M \tilde{c}_\gamma(m) \tilde{z}^{-m} \right)^{1/\gamma}, & -1 \le \gamma < 0 \\ \exp \displaystyle\sum_{m=0}^M \tilde{c}_\gamma(m) \tilde{z}^{-m}, & \gamma = 0 \end{array} \right. \end{eqnarray}\end{split}\]where\[ \tilde{z}^{-1} = \frac{z^{-1} - \alpha}{1 - \alpha z^{-1}}. \]Public Functions
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MelGeneralizedCepstralAnalysis(int fft_length, int num_order, double alpha, double gamma, int num_iteration, double convergence_threshold)
- Parameters:
fft_length – [in] Number of FFT bins, \(N\).
num_order – [in] Order of cepstral coefficients, \(M\).
alpha – [in] All-pass constant, \(\alpha\).
gamma – [in] Exponent parameter, \(\gamma\).
num_iteration – [in] Number of iterations of Newton method, \(J\).
convergence_threshold – [in] Convergence threshold, \(\epsilon\).
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inline int GetFftLength() const
- Returns:
FFT length.
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inline int GetNumOrder() const
- Returns:
Order of coefficients.
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inline double GetAlpha() const
- Returns:
All-pass constant.
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inline double GetGamma() const
- Returns:
Gamma.
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inline int GetNumIteration() const
- Returns:
Number of iterations.
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inline double GetConvergenceThreshold() const
- Returns:
Convergence threshold.
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inline bool IsValid() const
- Returns:
True if this object is valid.
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bool Run(const std::vector<double> &periodogram, std::vector<double> *mel_generalized_cepstrum, MelGeneralizedCepstralAnalysis::Buffer *buffer) const
- Parameters:
periodogram – [in] \((N/2+1)\)-length periodogram.
mel_generalized_cepstrum – [out] \(M\)-th order mel-generalized cepstral coefficients.
buffer – [out] Buffer.
- Returns:
True on success, false on failure.
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class Buffer
Buffer for MelGeneralizedCepstralAnalysis class.
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MelGeneralizedCepstralAnalysis(int fft_length, int num_order, double alpha, double gamma, int num_iteration, double convergence_threshold)