# ------------------------------------------------------------------------ #
# Copyright 2022 SPTK Working Group #
# #
# Licensed under the Apache License, Version 2.0 (the "License"); #
# you may not use this file except in compliance with the License. #
# You may obtain a copy of the License at #
# #
# http://www.apache.org/licenses/LICENSE-2.0 #
# #
# Unless required by applicable law or agreed to in writing, software #
# distributed under the License is distributed on an "AS IS" BASIS, #
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. #
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import torch
from torch import nn
from ..misc.utils import remove_gain
[docs]
class Spectrum(nn.Module):
"""See `this page <https://sp-nitech.github.io/sptk/latest/main/spec.html>`_
for details.
Parameters
----------
fft_length : int >= 2
Number of FFT bins, :math:`L`.
eps : float >= 0
A small value added to power spectrum.
relative_floor : float < 0 or None
Relative floor in decibels.
out_format : ['db', 'log-magnitude', 'magnitude', 'power']
Output format.
"""
def __init__(self, fft_length, *, eps=0, relative_floor=None, out_format="power"):
super().__init__()
assert 2 <= fft_length
assert 0 <= eps
assert relative_floor is None or relative_floor < 0
self.fft_length = fft_length
self.eps = eps
self.relative_floor = self._precompute(relative_floor)
self.formatter = self._formatter(out_format)
[docs]
def forward(self, b=None, a=None):
"""Compute spectrum.
Parameters
----------
b : Tensor [shape=(..., M+1)] or None
Framed waveform or numerator coefficients.
a : Tensor [shape=(..., N+1)] or None
Denominator coefficients.
Returns
-------
out : Tensor [shape=(..., L/2+1)]
Spectrum.
Examples
--------
>>> x = diffsptk.ramp(1, 3)
>>> x
tensor([1., 2., 3.])
>>> spec = diffsptk.Spectrum(8)
>>> y = spec(x)
>>> y
tensor([36.0000, 25.3137, 8.0000, 2.6863, 4.0000])
"""
return self._forward(
b, a, self.fft_length, self.eps, self.relative_floor, self.formatter
)
@staticmethod
def _forward(b, a, fft_length, eps, relative_floor, formatter):
if b is None and a is None:
raise ValueError("Either b or a must be specified.")
if b is not None:
B = torch.fft.rfft(b, n=fft_length).abs()
if a is not None:
K, a = remove_gain(a, return_gain=True)
A = torch.fft.rfft(a, n=fft_length).abs()
if b is None:
X = K / A
elif a is None:
X = B
else:
X = K * (B / A)
s = torch.square(X) + eps
if relative_floor is not None:
m = torch.amax(s, dim=-1, keepdim=True)
s = torch.maximum(s, m * relative_floor)
s = formatter(s)
return s
@staticmethod
def _func(b, a, fft_length, eps, relative_floor, out_format):
relative_floor = Spectrum._precompute(relative_floor)
formatter = Spectrum._formatter(out_format)
return Spectrum._forward(b, a, fft_length, eps, relative_floor, formatter)
@staticmethod
def _precompute(relative_floor):
if relative_floor is None:
return None
return 10 ** (relative_floor / 10)
@staticmethod
def _formatter(out_format):
if out_format in (0, "db"):
return lambda x: 10 * torch.log10(x)
elif out_format in (1, "log-magnitude"):
return lambda x: 0.5 * torch.log(x)
elif out_format in (2, "magnitude"):
return lambda x: torch.sqrt(x)
elif out_format in (3, "power"):
return lambda x: x
raise ValueError(f"out_format {out_format} is not supported.")