freqt

Functions

int main(int argc, char *argv[])

freqt [ option ] [ infile ]

-m int
- order of minimum phase sequence $(0 \leq M_{1})$
-M int
- order of warped sequence $(0 \leq M_{2})$
-a double
- all-pass constant of input sequence $(| α_{1} | < 1)$
-A double
- all-pass constant of output sequence $(| α_{2} | < 1)$
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

mgc2mgc

class 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_{α_{1}} (0), & c_{α_{1}} (1), & \dots, & c_{α_{1}} (M_{1}), \end{array}

and the output is the

M_{2}

-th order frequency-warped sequence:

\begin{array}{cccc} c_{α_{2}} (0), & c_{α_{2}} (1), & \dots, & c_{α_{2}} (M_{2}) . \end{array}

The output sequence can be obtained by using the following recursion formula:

\begin{array}{r} c_{α_{2}}^{(i)} (m) = {\begin{cases} c_{α_{1}} (- i) + α c_{α_{2}}^{(i - 1)} (0), & m = 0 \\ (1 - α^{2}) c_{α_{2}}^{(i - 1)} (0) + α c_{α_{2}}^{(i - 1)} (1), & m = 1 \\ c_{α_{2}}^{(i - 1)} (m - 1) + α (c_{α_{2}}^{(i - 1)} (m) - c_{α_{2}}^{(i)} (m - 1)), & m = 2, 3, \dots, M_{2} \end{cases} \\ i = - M_{1}, \dots, - 1, 0 \end{array}

where

α = (α_{2} - α_{1}) / (1 - α_{1} α_{2}) .

The initial condition of the recursion is

c_{α_{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

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, $α$ .

inline int GetNumInputOrder() const

Returns:: Order of input.

inline int GetNumOutputOrder() const

Returns:: Order of output.

inline double GetAlpha() const

Returns:: Frequency warping factor.

inline bool IsValid() const

Returns:: True if this object is valid.

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.

class Buffer: Buffer for FrequencyTransform class.