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
235
|
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# ROCOF test waveform library\n",
"\n",
"This is a re-implementation of the ROCOF test waveforms described in https://zenodo.org/record/3559798\n",
"\n",
"**This file is exported as a python module and loaded from other notebooks here, so please make sure to re-export when changing it.**"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"import math\n",
"import itertools\n",
"\n",
"import numpy as np\n",
"from scipy import signal\n",
"from matplotlib import pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib notebook"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"def sample_waveform(generator, duration:\"s\"=10, sampling_rate:\"sp/s\"=10000, frequency:\"Hz\"=50):\n",
" samples = int(duration*sampling_rate)\n",
" phases = np.linspace(0, 2*np.pi, 6, endpoint=False)\n",
" omega_t = np.linspace(phases, phases + 2*np.pi*duration*frequency, samples)\n",
" fundamental = np.sin(omega_t)\n",
" return generator(omega_t, fundamental, sampling_rate=sampling_rate, duration=duration, frequency=frequency).swapaxes(0, 1)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"def gen_harmonics(amplitudes, phases=[]):\n",
" return lambda omega_t, fundamental, **_: fundamental + np.sum([\n",
" a*np.sin((p if p else 0) + i*omega_t)\n",
" for i, (a, p) in enumerate(itertools.zip_longest(amplitudes, phases), start=2)\n",
" ], axis=0)\n",
"\n",
"def test_harmonics():\n",
" return gen_harmonics([0.02, 0.05, 0.01, 0.06, 0.005, 0.05, 0.005, 0.015, 0.005, 0.035, 0.005, 0.003])"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"def gen_interharmonic(amplitudes, ih=[], ih_phase=[]):\n",
" def gen(omega_t, fundamental, **_):\n",
" return fundamental + np.sum([\n",
" a*np.sin(omega_t * ih + (p if p else 0))\n",
" for a, ih, p in itertools.zip_longest(amplitudes, ih, ih_phase)\n",
" ], axis=0)\n",
" return gen\n",
"\n",
"def test_interharmonics():\n",
" return gen_interharmonic([0.1], [15.01401], [np.pi])"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"def gen_noise(amplitude=0.2, fmax:'Hz'=4.9e3, fmin:'Hz'=100, filter_order=6):\n",
" def gen(omega_t, fundamental, sampling_rate, **_):\n",
" noise = np.random.normal(0, amplitude, fundamental.shape)\n",
" b, a = signal.butter(filter_order,\n",
" [fmin, min(fmax, sampling_rate//2-1)],\n",
" btype='bandpass',\n",
" fs=sampling_rate)\n",
" return fundamental + signal.lfilter(b, a, noise, axis=0)\n",
" return gen\n",
"\n",
"def test_noise():\n",
" return gen_noise()\n",
"\n",
"def test_noise_loud():\n",
" return gen_noise(amplitude=0.5, fmin=10)"
]
},
{
"cell_type": "code",
"execution_count": 406,
"metadata": {},
"outputs": [],
"source": [
"def gen_steps(size_amplitude=0.1, size_phase=0.1*np.pi, steps_per_sec=1):\n",
" def gen(omega_t, fundamental, duration, **_):\n",
" n = int(steps_per_sec * duration)\n",
" indices = np.random.randint(0, len(omega_t), n)\n",
" amplitudes = np.random.normal(1, size_amplitude, (n, 6))\n",
" phases = np.random.normal(0, size_phase, (n, 6))\n",
" amplitude = np.ones(omega_t.shape)\n",
" for start, end, a, p in zip(indices, indices[1:], amplitudes, phases):\n",
" omega_t[start:end] += p\n",
" amplitude[start:end] = a\n",
" return amplitude*np.sin(omega_t)\n",
" return gen\n",
"\n",
"def test_amplitude_steps():\n",
" return gen_steps(size_amplitude=0.4, size_phase=0)\n",
"\n",
"def test_phase_steps():\n",
" return gen_steps(size_amplitude=0, size_phase=0.1)\n",
"\n",
"def test_amplitude_and_phase_steps():\n",
" return gen_steps(size_amplitude=0.2, size_phase=0.07)"
]
},
{
"cell_type": "code",
"execution_count": 418,
"metadata": {},
"outputs": [],
"source": [
"def step_gen(shape, stdev, duration, steps_per_sec=1.0, mean=0.0):\n",
" samples, channels = shape\n",
" n = int(steps_per_sec * duration)\n",
" indices = np.random.randint(0, samples, n)\n",
" phases = np.random.normal(mean, stdev, (n, 6))\n",
" amplitude = np.ones((samples, channels))\n",
" out = np.zeros(shape)\n",
" for start, end, a in zip(indices, indices[1:], amplitude):\n",
" out[start:end] = a\n",
" return out\n",
"\n",
"def gen_chirp(fmin, fmax, period, dwell_time=1.0, amplitude=None, phase_steps=None):\n",
" def gen(omega_t, fundamental, sampling_rate, duration, **_):\n",
" samples = int(duration*sampling_rate)\n",
" phases = np.linspace(0, 2*np.pi, 6, endpoint=False)\n",
" \n",
" c = (fmax-fmin)/period\n",
" t = np.linspace(0, duration, samples)\n",
" \n",
" x = np.repeat(np.reshape(2*np.pi*fmin*t, (-1,1)), 6, axis=1)\n",
" data = (phases + x)[:int(sampling_rate*dwell_time)]\n",
" current_phase = 2*np.pi*fmin*dwell_time\n",
" direction = 'up'\n",
" \n",
" for idx in range(int(dwell_time*sampling_rate), samples, int(2*period*sampling_rate)):\n",
" t1 = np.linspace(0, period, int(period*sampling_rate))\n",
" t2 = np.linspace(0, period, int(period*sampling_rate))\n",
" chirp_phase = np.hstack((\n",
" 2*np.pi*(c/2 * t1**2 + fmin * t1),\n",
" 2*np.pi*(-c/2 * t2**2 + fmax * t2 - (c/2 * period**2 + fmin * period))\n",
" ))\n",
" chirp_phase = np.repeat(np.reshape(chirp_phase, (-1, 1)), 6, axis=1)\n",
" new = phases + chirp_phase + current_phase\n",
" current_phase = chirp_phase[-1]\n",
" data = np.vstack((data, new))\n",
" \n",
" data = data[:len(fundamental)]\n",
" \n",
" if phase_steps:\n",
" (step_amplitude, steps_per_sec) = phase_steps\n",
" steps = step_gen(data.shape, step_amplitude, duration, steps_per_sec)\n",
" data += steps\n",
" \n",
" if amplitude is None:\n",
" return np.sin(data)\n",
" else:\n",
" return fundamental + amplitude*np.sin(data)\n",
" return gen\n",
"\n",
"def test_close_interharmonics_and_flicker():\n",
" return gen_chirp(90.0, 150.0, 10, 1, amplitude=0.1)\n",
"\n",
"def test_off_frequency():\n",
"# return gen_chirp(48.0, 52.0, 0.25, 1)\n",
" return gen_chirp(48.0, 52.0, 10, 1)\n",
"\n",
"def test_sweep_phase_steps():\n",
" return gen_chirp(48.0, 52.0, 10, 1, phase_steps=(0.1, 1))\n",
"# return gen_chirp(48.0, 52.0, 0.25, 1, phase_steps=(0.1, 1))"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"all_tests = [test_harmonics, test_interharmonics, test_noise, test_noise_loud, test_amplitude_steps, test_phase_steps, test_amplitude_and_phase_steps, test_close_interharmonics_and_flicker, test_off_frequency, test_sweep_phase_steps]"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.5"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
|
