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
|
#!/usr/bin/env python
#
# Generate an example RX and TX dataset, with a subsample delay and try to resolve it afterwards
#
#
# The MIT License (MIT)
#
# Copyright (c) 2017 Matthias P. Braendli
#
# Permission is hereby granted, free of charge, to any person obtaining a copy
# of this software and associated documentation files (the "Software"), to deal
# in the Software without restriction, including without limitation the rights
# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
# copies of the Software, and to permit persons to whom the Software is
# furnished to do so, subject to the following conditions:
#
# The above copyright notice and this permission notice shall be included in all
# copies or substantial portions of the Software.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
# SOFTWARE.
import matplotlib.pyplot as plt
import scipy
import scipy.signal
import numpy as np
def gen_omega(length):
if not length % 2 == 0:
raise ValueError('Needs an even length array.')
halflength = int(length/2)
omega = np.zeros(length)
omega[0:halflength] = 2*np.pi*np.arange(halflength)
omega[halflength+1:] = 2*np.pi*( np.arange(halflength+1, length)-length )
return omega / length
def gen_signals(oversample, delay):
"""Generate a signal that is delayed and a bit noisy. Returns a tuple
(original signal, shifted signal)"""
iq_file = "/home/bram/dab/aux/odr-dab-cir/phasereference.2048000.fc64.iq"
iq_data = np.fromfile(iq_file, np.complex64)
# oversampling the input signal doesn't make much of a difference
phase_ref_iq = scipy.signal.resample(iq_data, 2 * len(iq_data))
# make the signal periodic by duplicating the signal
phase_ref_iq = np.concatenate((phase_ref_iq, phase_ref_iq))
noise_iq = np.random.normal(scale = np.max(np.abs(phase_ref_iq)) * 0.02,
size=len(phase_ref_iq))
phase_ref_iq = phase_ref_iq + noise_iq
# exp(-2i pi f) is the Fourier transform of a unity delay.
# exp(2i pi f) is a negative delay.
bin_frequencies = np.concatenate(
(np.linspace(0, 0.5, len(phase_ref_iq)/2, endpoint=False),
np.linspace(-0.5, 0, len(phase_ref_iq)/2, endpoint=False)))
phase_ref_uc = scipy.signal.resample(phase_ref_iq, oversample * len(phase_ref_iq))
phase_ref_uc_delayed = np.roll(phase_ref_uc, -delay)
phase_ref_delayed = scipy.signal.resample(phase_ref_uc_delayed, len(phase_ref_iq))
return phase_ref_iq, phase_ref_delayed
def arg_max_corr(a, b):
"""Calculate fractional delay giving max correlation between a and b"""
if len(a.shape) > 1:
raise ValueError('Needs a 1-dimensional array.')
length = len(a)
if not length % 2 == 0:
raise ValueError('Needs an even length array.')
halflength = int(length/2)
if not a.shape == b.shape:
raise ValueError('The 2 arrays need to be the same shape')
# Start by finding the coarse discretised arg_max
coarse_max = np.argmax(np.correlate(a, b, mode='full')) - length+1
omega = gen_omega(length)
fft_a = np.fft.fft(a)
def correlate_point(tau):
rotate_vec = np.exp(1j*tau*omega)
rotate_vec[halflength] = np.cos(np.pi*tau)
return np.sum((np.fft.ifft(fft_a*rotate_vec)).real*b)
start_arg, end_arg = (float(coarse_max)-1, float(coarse_max)+1)
max_arg = scipy.optimize.fminbound(lambda tau: -correlate_point(tau),
start_arg, end_arg)
return np.real(max_arg)
def delay_signal(sig, delay):
"""Apply the delay calculated by arg_max_corr to sig"""
frac_delay, int_delay = np.modf(delay)
int_delay = int(int_delay)
print("Correcting integer delay {}".format(int_delay))
sig = np.roll(sig, int_delay)
print("Correcting fractional delay {}".format(frac_delay))
tau = -frac_delay
omega = gen_omega(len(sig))
sig_fft = np.fft.fft(sig)
rotate_vec = np.exp(1j*tau*omega)
rotate_vec[int(len(sig)/2)] = np.cos(np.pi*tau)
return np.fft.ifft(sig_fft * rotate_vec)
def fftplot(sig):
plt.plot(np.abs(np.fft.fftshift(np.fft.fft(sig))))
if __name__ == '__main__':
# Add a delay of d/oversample samples to the input signal
# by how much to oversample the signal before applying the delay
oversample = 8
do_plot = False
for d in [2, 7]:
a, b = gen_signals(d, oversample)
delay = arg_max_corr(a,b)
print("{} {}".format(d / oversample, delay))
print("{} {}".format(d / oversample, arg_max_corr(a, delay_signal(b, delay))))
if do_plot:
plt.figure()
fftplot(a)
fftplot(a-b)
if do_plot:
plt.show()
|
