freqt2#

class diffsptk.SecondOrderAllPassFrequencyTransform(in_order: int, out_order: int, alpha: float = 0, theta: float = 0, n_fft: int = 512, device: device | None = None, dtype: dtype | None = None)[source]#

Second-order all-pass frequency transform module.

Parameters:

in_orderint >= 0: The order of the input sequence, \(M_1\).
out_orderint >= 0: The order of the output sequence, \(M_2\).
alphafloat in (-1, 1): The frequency warping factor, \(\alpha\).
thetafloat in [0, 1]: The emphasis frequency, \(\theta\).
n_fftint >> M2: The number of FFT bins. The accurate conversion requires the large value.
devicetorch.device or None: The device of this module.
dtypetorch.dtype or None: The data type of this module.

References

[1]

T. Wakako et al., “Speech spectral estimation based on expansion of log spectrum by arbitrary basis functions,” IEICE Trans, vol. J82-D-II, no. 12, pp. 2203-2211, 1999 (in Japanese).

forward(c: Tensor) → Tensor[source]#

Perform second-order all-pass frequency transform.

Parameters:

cTensor [shape=(…, M1+1)]: The input sequence.

Returns:

outTensor [shape=(…, M2+1)]: The warped sequence.

Examples

>>> import diffsptk
>>> import torch
>>> freqt2 = diffsptk.SecondOrderAllPassFrequencyTransform(
...     3, 4, alpha=0.1, theta=0.3
... )
>>> c1 = torch.tensor([0.8, 0.6, -1.0, -0.5])
>>> c2 = freqt2(c1)
>>> c2
tensor([ 0.8388,  0.4785, -1.1090, -0.3654,  0.0682])

diffsptk.functional.freqt2(c: Tensor, out_order: int, alpha: float = 0, theta: float = 0, n_fft: int = 512) → Tensor[source]#

Perform second-order all-pass frequency transform.

Parameters:

cTensor [shape=(…, M1+1)]: The cepstral coefficients.
out_orderint >= 0: The order of the output sequence, \(M_2\).
alphafloat in (-1, 1): The frequency warping factor, \(\alpha\).
thetafloat in [0, 1]: The emphasis frequency, \(\theta\).
n_fftint >> M2: The number of FFT bins. The accurate conversion requires the large value.

Returns:

outTensor [shape=(…, M2+1)]: The warped cepstral coefficients.