c2acr

Functions

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

c2acr [ option ] [ infile ]

• -m int

  • order of cepstral coefficients $(0\le M_1<L)$

• -M int

  • order of autocorrelation coefficients $(0\le M_2<L)$

• -l int

  • FFT length $(2\le L)$

• infile str

  • double-type cepstral coefficients

• stdout

  • double-type autocorrelation coefficients

The following example converts the 30-th order cepstral coefficients in data.cep into the 15-th order LPC coefficients.

c2acr -m 30 -M 15 < data.cep | levdur -m 15 > data.lpc

Parameters:

• argc – [in] Number of arguments.

• argv – [in] Argument vector.

Returns:

0 on success, 1 on failure.

See also

lpc2c acorr

class CepstrumToAutocorrelation

Convert cepstral coefficients to autocorrelation coefficients.

The input is the $M_1$-th order cepstral coefficients:

$$\begin{array}{cccc}c(0),& c(1),& \dots ,& c(M_1),\end{array}$$

and the output is the $M_2$-th order autocorrelation coefficients:

$$\begin{array}{cccc}r(0),& r(1),& \dots ,& r(M_2),\end{array}$$

The definition of the cepstrum can be represented as

$$c(m)={\mathcal{F}}^{-1}\{\log |\mathcal{F}\{x(m)\}|\},$$

where $x(m)$ is a signal, ${\mathcal{F}}^{-1}$ and $\mathcal{F}$ denote the DFT and the inverse DFT, respectively. From the definition, the relation between the cepstrum and the autocorrelation can be derived as follows:

$$\begin{array}{r}\begin{array}{rcl}c(m)& =& {\mathcal{F}}^{-1}\{\frac{1}{2}\log |X(\omega ){|}^2\}\\ & =& {\mathcal{F}}^{-1}\{\frac{1}{2}\log \mathcal{F}\{r(m)\}\},\end{array}\end{array}$$

where the Wiener–Khinchin theorem is used. Thus

$$r(m)={\mathcal{F}}^{-1}\{\exp (2\mathcal{F}\{c(m)\})\}.$$

Note that the imaginary part is zero.

Public Functions

CepstrumToAutocorrelation(int num_input_order, int num_output_order, int fft_length)

Parameters:

• num_input_order – [in] Order of cepstral coefficients, $M_1$.

• num_output_order – [in] Order of autocorrelation coefficients, $M_2$.

• fft_length – [in] FFT length.

inline int GetNumInputOrder() const

Returns:

Order of cepstral coefficients.

inline int GetNumOutputOrder() const

Returns:

Order of autocorrelation coefficients.

inline int GetFftLength() const

Returns:

FFT length.

inline bool IsValid() const

Returns:

True if this object is valid.

bool Run(const std::vector<double> &cepstrum, std::vector<double> *autocorrelation, CepstrumToAutocorrelation::Buffer *buffer) const

Parameters:

• cepstrum – [in] $M_1$-th order cesptral coefficients.

• autocorrelation – [out] $M_2$-th order autocorrelation coefficients.

• buffer – [out] Buffer.

Returns:

True on success, false on failure.

class Buffer

Buffer for CepstrumToAutocorrelation class.