-
-
Notifications
You must be signed in to change notification settings - Fork 43.9k
/
butterworth_filter.py
234 lines (193 loc) · 5.85 KB
/
butterworth_filter.py
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
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
from math import cos, sin, sqrt, tau
from audio_filters.iir_filter import IIRFilter
"""
Create 2nd-order IIR filters with Butterworth design.
Code based on https://webaudio.github.io/Audio-EQ-Cookbook/audio-eq-cookbook.html
Alternatively you can use scipy.signal.butter, which should yield the same results.
"""
def make_lowpass(
frequency: int,
samplerate: int,
q_factor: float = 1 / sqrt(2),
) -> IIRFilter:
"""
Creates a low-pass filter
>>> filter = make_lowpass(1000, 48000)
>>> filter.a_coeffs + filter.b_coeffs # doctest: +NORMALIZE_WHITESPACE
[1.0922959556412573, -1.9828897227476208, 0.9077040443587427, 0.004277569313094809,
0.008555138626189618, 0.004277569313094809]
"""
w0 = tau * frequency / samplerate
_sin = sin(w0)
_cos = cos(w0)
alpha = _sin / (2 * q_factor)
b0 = (1 - _cos) / 2
b1 = 1 - _cos
a0 = 1 + alpha
a1 = -2 * _cos
a2 = 1 - alpha
filt = IIRFilter(2)
filt.set_coefficients([a0, a1, a2], [b0, b1, b0])
return filt
def make_highpass(
frequency: int,
samplerate: int,
q_factor: float = 1 / sqrt(2),
) -> IIRFilter:
"""
Creates a high-pass filter
>>> filter = make_highpass(1000, 48000)
>>> filter.a_coeffs + filter.b_coeffs # doctest: +NORMALIZE_WHITESPACE
[1.0922959556412573, -1.9828897227476208, 0.9077040443587427, 0.9957224306869052,
-1.9914448613738105, 0.9957224306869052]
"""
w0 = tau * frequency / samplerate
_sin = sin(w0)
_cos = cos(w0)
alpha = _sin / (2 * q_factor)
b0 = (1 + _cos) / 2
b1 = -1 - _cos
a0 = 1 + alpha
a1 = -2 * _cos
a2 = 1 - alpha
filt = IIRFilter(2)
filt.set_coefficients([a0, a1, a2], [b0, b1, b0])
return filt
def make_bandpass(
frequency: int,
samplerate: int,
q_factor: float = 1 / sqrt(2),
) -> IIRFilter:
"""
Creates a band-pass filter
>>> filter = make_bandpass(1000, 48000)
>>> filter.a_coeffs + filter.b_coeffs # doctest: +NORMALIZE_WHITESPACE
[1.0922959556412573, -1.9828897227476208, 0.9077040443587427, 0.06526309611002579,
0, -0.06526309611002579]
"""
w0 = tau * frequency / samplerate
_sin = sin(w0)
_cos = cos(w0)
alpha = _sin / (2 * q_factor)
b0 = _sin / 2
b1 = 0
b2 = -b0
a0 = 1 + alpha
a1 = -2 * _cos
a2 = 1 - alpha
filt = IIRFilter(2)
filt.set_coefficients([a0, a1, a2], [b0, b1, b2])
return filt
def make_allpass(
frequency: int,
samplerate: int,
q_factor: float = 1 / sqrt(2),
) -> IIRFilter:
"""
Creates an all-pass filter
>>> filter = make_allpass(1000, 48000)
>>> filter.a_coeffs + filter.b_coeffs # doctest: +NORMALIZE_WHITESPACE
[1.0922959556412573, -1.9828897227476208, 0.9077040443587427, 0.9077040443587427,
-1.9828897227476208, 1.0922959556412573]
"""
w0 = tau * frequency / samplerate
_sin = sin(w0)
_cos = cos(w0)
alpha = _sin / (2 * q_factor)
b0 = 1 - alpha
b1 = -2 * _cos
b2 = 1 + alpha
filt = IIRFilter(2)
filt.set_coefficients([b2, b1, b0], [b0, b1, b2])
return filt
def make_peak(
frequency: int,
samplerate: int,
gain_db: float,
q_factor: float = 1 / sqrt(2),
) -> IIRFilter:
"""
Creates a peak filter
>>> filter = make_peak(1000, 48000, 6)
>>> filter.a_coeffs + filter.b_coeffs # doctest: +NORMALIZE_WHITESPACE
[1.0653405327119334, -1.9828897227476208, 0.9346594672880666, 1.1303715025601122,
-1.9828897227476208, 0.8696284974398878]
"""
w0 = tau * frequency / samplerate
_sin = sin(w0)
_cos = cos(w0)
alpha = _sin / (2 * q_factor)
big_a = 10 ** (gain_db / 40)
b0 = 1 + alpha * big_a
b1 = -2 * _cos
b2 = 1 - alpha * big_a
a0 = 1 + alpha / big_a
a1 = -2 * _cos
a2 = 1 - alpha / big_a
filt = IIRFilter(2)
filt.set_coefficients([a0, a1, a2], [b0, b1, b2])
return filt
def make_lowshelf(
frequency: int,
samplerate: int,
gain_db: float,
q_factor: float = 1 / sqrt(2),
) -> IIRFilter:
"""
Creates a low-shelf filter
>>> filter = make_lowshelf(1000, 48000, 6)
>>> filter.a_coeffs + filter.b_coeffs # doctest: +NORMALIZE_WHITESPACE
[3.0409336710888786, -5.608870992220748, 2.602157875636628, 3.139954022810743,
-5.591841778072785, 2.5201667380627257]
"""
w0 = tau * frequency / samplerate
_sin = sin(w0)
_cos = cos(w0)
alpha = _sin / (2 * q_factor)
big_a = 10 ** (gain_db / 40)
pmc = (big_a + 1) - (big_a - 1) * _cos
ppmc = (big_a + 1) + (big_a - 1) * _cos
mpc = (big_a - 1) - (big_a + 1) * _cos
pmpc = (big_a - 1) + (big_a + 1) * _cos
aa2 = 2 * sqrt(big_a) * alpha
b0 = big_a * (pmc + aa2)
b1 = 2 * big_a * mpc
b2 = big_a * (pmc - aa2)
a0 = ppmc + aa2
a1 = -2 * pmpc
a2 = ppmc - aa2
filt = IIRFilter(2)
filt.set_coefficients([a0, a1, a2], [b0, b1, b2])
return filt
def make_highshelf(
frequency: int,
samplerate: int,
gain_db: float,
q_factor: float = 1 / sqrt(2),
) -> IIRFilter:
"""
Creates a high-shelf filter
>>> filter = make_highshelf(1000, 48000, 6)
>>> filter.a_coeffs + filter.b_coeffs # doctest: +NORMALIZE_WHITESPACE
[2.2229172136088806, -3.9587208137297303, 1.7841414181566304, 4.295432981120543,
-7.922740859457287, 3.6756456963725253]
"""
w0 = tau * frequency / samplerate
_sin = sin(w0)
_cos = cos(w0)
alpha = _sin / (2 * q_factor)
big_a = 10 ** (gain_db / 40)
pmc = (big_a + 1) - (big_a - 1) * _cos
ppmc = (big_a + 1) + (big_a - 1) * _cos
mpc = (big_a - 1) - (big_a + 1) * _cos
pmpc = (big_a - 1) + (big_a + 1) * _cos
aa2 = 2 * sqrt(big_a) * alpha
b0 = big_a * (ppmc + aa2)
b1 = -2 * big_a * pmpc
b2 = big_a * (ppmc - aa2)
a0 = pmc + aa2
a1 = 2 * mpc
a2 = pmc - aa2
filt = IIRFilter(2)
filt.set_coefficients([a0, a1, a2], [b0, b1, b2])
return filt