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# Copyright 2022 SPTK Working Group #
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import torch
import torch.nn.functional as F
from scipy.special import comb
from ..utils.private import check_size
from ..utils.private import get_values
from ..utils.private import hankel
from ..utils.private import to
from ..utils.private import vander
from .base import BaseFunctionalModule
from .root_pol import PolynomialToRoots
[docs]
class AutocorrelationToCompositeSinusoidalModelCoefficients(BaseFunctionalModule):
"""See `this page <https://sp-nitech.github.io/sptk/latest/main/acr2csm.html>`_
for details.
Parameters
----------
acr_order : int >= 0
The order of the autocorrelation, :math:`M`.
References
----------
.. [1] S. Sagayama et al., "Duality theory of composite sinusoidal modeling and
linear prediction," *Proceedings of ICASSP*, pp. 1261-1264, 1986.
"""
def __init__(self, acr_order):
super().__init__()
self.in_dim = acr_order + 1
_, _, tensors = self._precompute(*get_values(locals()))
self.register_buffer("C", tensors[0])
[docs]
def forward(self, r):
"""Convert autocorrelation to CSM coefficients.
Parameters
----------
r : Tensor [shape=(..., M+1)]
The autocorrelation.
Returns
-------
out : Tensor [shape=(..., M+1)]
The CSM coefficients.
Examples
--------
>>> x = diffsptk.nrand(4)
>>> x
tensor([ 0.0165, -2.3693, 0.1375, -0.2262, 1.3307])
>>> acorr = diffsptk.Autocorrelation(5, 3)
>>> acr2csm = diffsptk.AutocorrelationToCompositeSinusoidalModelCoefficients(3)
>>> c = acr2csm(acorr(x))
>>> c
tensor([0.9028, 2.5877, 3.8392, 3.6153])
"""
check_size(r.size(-1), self.in_dim, "dimension of autocorrelation")
return self._forward(r, **self._buffers)
@staticmethod
def _func(r, *args, **kwargs):
_, _, tensors = (
AutocorrelationToCompositeSinusoidalModelCoefficients._precompute(
r.size(-1) - 1, *args, **kwargs, device=r.device, dtype=r.dtype
)
)
return AutocorrelationToCompositeSinusoidalModelCoefficients._forward(
r, *tensors
)
@staticmethod
def _takes_input_size():
return True
@staticmethod
def _check(acr_order):
if acr_order <= 0 or acr_order % 2 == 0:
raise ValueError("acr_order must be a positive odd number.")
if 30 < acr_order:
raise ValueError("acr_order must be small due to computational accuracy.")
@staticmethod
def _precompute(acr_order, device=None, dtype=None):
AutocorrelationToCompositeSinusoidalModelCoefficients._check(acr_order)
N = acr_order + 1
B = torch.zeros((N, N), device=device, dtype=torch.double)
for n in range(N):
z = 2**-n
for k in range(n + 1):
B[k, n] = comb(n, k, exact=True) * z
C = torch.zeros((N, N), device=device, dtype=torch.double)
for k in range(N):
bias = k % 2
center = k // 2
length = center + 1
C[bias : bias + 2 * length : 2, k] = B[
bias + center : bias + center + length, k
]
C[1:] *= 2
return None, None, (to(C, dtype=dtype),)
@staticmethod
def _forward(r, C):
if r.dtype != torch.double or C.dtype != torch.double:
raise ValueError("Only double precision is supported.")
u = torch.matmul(r, C)
u1, u2 = torch.tensor_split(u, 2, dim=-1)
U = hankel(-u)
p = torch.matmul(U.inverse(), u2.unsqueeze(-1)).squeeze(-1)
x = PolynomialToRoots._func(F.pad(p.flip(-1), (1, 0), value=1))
x, _ = torch.sort(x.real, descending=True)
w = torch.acos(x)
V = vander(x)
m = torch.matmul(V.inverse(), u1.unsqueeze(-1)).squeeze(-1)
c = torch.cat((w, m), dim=-1)
return c