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# Copyright 2020 Tomoki Hayashi
# MIT License (https://opensource.org/licenses/MIT)
"""Pseudo QMF modules."""
import numpy as np
import torch
import torch.nn.functional as F
from scipy.signal import kaiser
def design_prototype_filter(taps=62, cutoff_ratio=0.15, 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
class PQMF(torch.nn.Module):
"""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, device, subbands=8, taps=62, cutoff_ratio=0.15, beta=9.0):
"""Initialize PQMF module.
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__()
# define filter coefficient
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 - 1) / 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 - 1) / 2))
- (-1) ** k * np.pi / 4
)
)
# convert to tensor
analysis_filter = torch.from_numpy(h_analysis).float().unsqueeze(1).to(device)
synthesis_filter = torch.from_numpy(h_synthesis).float().unsqueeze(0).to(device)
# register coefficients as buffer
self.register_buffer("analysis_filter", analysis_filter)
self.register_buffer("synthesis_filter", synthesis_filter)
# filter for downsampling & upsampling
updown_filter = torch.zeros((subbands, subbands, subbands)).float().to(device)
for k in range(subbands):
updown_filter[k, k, 0] = 1.0
self.register_buffer("updown_filter", updown_filter)
self.subbands = subbands
# keep padding info
self.pad_fn = torch.nn.ConstantPad1d(taps // 2, 0.0)
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)
def synthesis(self, x):
"""Synthesis with PQMF.
Args:
x (Tensor): Input tensor (B, subbands, T // subbands).
Returns:
Tensor: Output tensor (B, 1, T).
"""
# NOTE(kan-bayashi): Power will be dreased so here multiply by # subbands.
# Not sure this is the correct way, it is better to check again.
# TODO(kan-bayashi): Understand the reconstruction procedure
x = F.conv_transpose1d(
x, self.updown_filter * self.subbands, stride=self.subbands
)
return F.conv1d(self.pad_fn(x), self.synthesis_filter)
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