freqt
Functions
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int main(int argc, char *argv[])
freqt [ option ] [ infile ]
-m int
order of minimum phase sequence \((0 \le M_1)\)
-M int
order of warped sequence \((0 \le M_2)\)
-a double
all-pass constant of input sequence \((|\alpha_1|<1)\)
-A double
all-pass constant of output sequence \((|\alpha_2|<1)\)
infile str
double-type minimum phase sequence
stdout
double-type warped sequence
The below example converts LPC coefficients into LPC mel-cepstral coefficients:
lpc2c < data.lpc | freqt -A 0.42 > data.lpcmc
The converted LPC mel-cepstral coefficients can be reverted if \(M_2\) is sufficiently greater than \(M_1\):
freqt -A -0.42 < data.lpcmc > data.lpc
- Parameters
argc – [in] Number of arguments.
argv – [in] Argument vector.
- Returns
0 on success, 1 on failure.
See also
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class sptk::FrequencyTransform
Transform a minimum phase sequence into a frequency-warped sequence.
The input is the \(M_1\)-th order minimum phase sequence:
\[ \begin{array}{cccc} c_{\alpha_1}(0), & c_{\alpha_1}(1), & \ldots, & c_{\alpha_1}(M_1), \end{array} \]and the output is the \(M_2\)-th order frequency-warped sequence:\[ \begin{array}{cccc} c_{\alpha_2}(0), & c_{\alpha_2}(1), & \ldots, & c_{\alpha_2}(M_2). \end{array} \]The output sequence can be obtained by using the following recursion formula:\[\begin{split} c_{\alpha_2}^{(i)}(m) = \left\{\begin{array}{ll} c_{\alpha_1}(-i) + \alpha\,c_{\alpha_2}^{(i-1)}(0), & m=0 \\ (1-\alpha^2)\,c_{\alpha_2}^{(i-1)}(0) + \alpha\,c_{\alpha_2}^{(i-1)}(1), & m=1 \\ c_{\alpha_2}^{(i-1)}(m-1) + \alpha (c_{\alpha_2}^{(i-1)}(m) - c_{\alpha_2}^{(i)}(m-1)), & m=2,3,\ldots,M_2 \end{array} \right. \\ i = -M_1,\ldots,-1,0 \end{split}\]where\[ \alpha = (\alpha_2 - \alpha_1)\,/\,(1 - \alpha_1 \alpha_2). \]The initial condition of the recursion is \(c_{\alpha_2}^{(-M_1-1)}(m) = 0\) for any \(m\).The transformation is based on the cascade of all-pass networks. For more detail, see [1]. Note that the above recursion can be represented as a linear transformation, i.e., matrix multiplication.
[1] A. Oppenheim and D. Johnson, “Discrete representation of signals,” Proc. of the IEEE, vol. 60, no. 6, pp. 681-691, 1972.
[2] K. Tokuda, T. Kobayashi, T. Masuko, and S. Imai, “Mel-generalized cepstral representation of speech - A unified approach to speech spectral estimation,” Proc. of ICSLP 1994, pp. 1043-1046, 1994.
Public Functions
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FrequencyTransform(int num_input_order, int num_output_order, double alpha)
- Parameters
num_input_order – [in] Order of input, \(M_1\).
num_output_order – [in] Order of output, \(M_2\).
alpha – [in] Frequency warping factor, \(\alpha\).
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inline int GetNumInputOrder() const
- Returns
Order of input.
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inline int GetNumOutputOrder() const
- Returns
Order of output.
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inline double GetAlpha() const
- Returns
Frequency warping factor.
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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> &minimum_phase_sequence, std::vector<double> *warped_sequence, FrequencyTransform::Buffer *buffer) const
- Parameters
minimum_phase_sequence – [in] \(M_1\)-th order input sequence.
warped_sequence – [out] \(M_2\)-th order output sequence.
buffer – [out] Buffer.
- Returns
True on success, false on failure.
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class Buffer
Buffer for FrequencyTransform class.
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FrequencyTransform(int num_input_order, int num_output_order, double alpha)