File size: 4,252 Bytes
26925fd
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
# -*- coding: utf-8 -*-

# 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, subbands=4, taps=62, cutoff_ratio=0.15, beta=9.0):
        """Initilize 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(PQMF, self).__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)
        synthesis_filter = torch.from_numpy(h_synthesis).float().unsqueeze(0)

        # register coefficients as beffer
        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()
        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).

        """
        x = F.conv_transpose1d(x, self.updown_filter * self.subbands, stride=self.subbands)
        return F.conv1d(self.pad_fn(x), self.synthesis_filter)