# Copyright (c) 2021 PaddlePaddle Authors. All Rights Reserved.
#
# 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.
# See the License for the specific language governing permissions and
# limitations under the License.
# Modified from espnet(https://github.com/espnet/espnet)
"""Pseudo QMF modules."""
import numpy as np
import paddle
import paddle.nn.functional as F
from paddle import nn
from scipy.signal import kaiser
[docs]def design_prototype_filter(taps=62, cutoff_ratio=0.142, beta=9.0):
"""Design prototype filter for PQMF.
This method is based on `A Kaiser window approach for the design of prototype
filters of cosine modulated filterbanks`_.
Args:
taps (int):
The number of filter taps.
cutoff_ratio (float):
Cut-off frequency ratio.
beta (float):
Beta coefficient for kaiser window.
Returns:
ndarray:
Impluse response of prototype filter (taps + 1,).
.. _`A Kaiser window approach for the design of prototype filters of cosine modulated filterbanks`:
https://ieeexplore.ieee.org/abstract/document/681427
"""
# check the arguments are valid
assert taps % 2 == 0, "The number of taps mush be even number."
assert 0.0 < cutoff_ratio < 1.0, "Cutoff ratio must be > 0.0 and < 1.0."
# make initial filter
omega_c = np.pi * cutoff_ratio
with np.errstate(invalid="ignore"):
h_i = np.sin(omega_c * (np.arange(taps + 1) - 0.5 * taps)) / (
np.pi * (np.arange(taps + 1) - 0.5 * taps))
h_i[taps //
2] = np.cos(0) * cutoff_ratio # fix nan due to indeterminate form
# apply kaiser window
w = kaiser(taps + 1, beta)
h = h_i * w
return h
[docs]class PQMF(nn.Layer):
"""PQMF module.
This module is based on `Near-perfect-reconstruction pseudo-QMF banks`_.
.. _`Near-perfect-reconstruction pseudo-QMF banks`:
https://ieeexplore.ieee.org/document/258122
"""
def __init__(self, subbands=4, taps=62, cutoff_ratio=0.142, beta=9.0):
"""Initilize PQMF module.
The cutoff_ratio and beta parameters are optimized for #subbands = 4.
See dicussion in https://github.com/kan-bayashi/ParallelWaveGAN/issues/195.
Args:
subbands (int):
The number of subbands.
taps (int):
The number of filter taps.
cutoff_ratio (float):
Cut-off frequency ratio.
beta (float):
Beta coefficient for kaiser window.
"""
super().__init__()
h_proto = design_prototype_filter(taps, cutoff_ratio, beta)
h_analysis = np.zeros((subbands, len(h_proto)))
h_synthesis = np.zeros((subbands, len(h_proto)))
for k in range(subbands):
h_analysis[k] = (
2 * h_proto * np.cos((2 * k + 1) * (np.pi / (2 * subbands)) * (
np.arange(taps + 1) - (taps / 2)) + (-1)**k * np.pi / 4))
h_synthesis[k] = (
2 * h_proto * np.cos((2 * k + 1) * (np.pi / (2 * subbands)) * (
np.arange(taps + 1) - (taps / 2)) - (-1)**k * np.pi / 4))
# convert to tensor
self.analysis_filter = paddle.to_tensor(
h_analysis, dtype="float32").unsqueeze(1)
self.synthesis_filter = paddle.to_tensor(
h_synthesis, dtype="float32").unsqueeze(0)
# filter for downsampling & upsampling
updown_filter = paddle.zeros(
(subbands, subbands, subbands), dtype="float32")
for k in range(subbands):
updown_filter[k, k, 0] = 1.0
self.updown_filter = updown_filter
self.subbands = subbands
# keep padding info
self.pad_fn = nn.Pad1D(taps // 2, mode='constant', value=0.0)
[docs] def analysis(self, x):
"""Analysis with PQMF.
Args:
x (Tensor):
Input tensor (B, 1, T).
Returns:
Tensor: Output tensor (B, subbands, T // subbands).
"""
x = F.conv1d(self.pad_fn(x), self.analysis_filter)
return F.conv1d(x, self.updown_filter, stride=self.subbands)
[docs] def synthesis(self, x):
"""Synthesis with PQMF.
Args:
x (Tensor):
Input tensor (B, subbands, T // subbands).
Returns:
Tensor: Output tensor (B, 1, T).
"""
x = F.conv1d_transpose(
x, self.updown_filter * self.subbands, stride=self.subbands)
return F.conv1d(self.pad_fn(x), self.synthesis_filter)
# when converting dygraph to static graph, can not use self.pqmf.synthesis directly
[docs] def forward(self, x):
return self.synthesis(x)