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
|
# -*- coding: utf-8 -*-
#
# DPD Computation Engine, utility to do subsample alignment.
#
# http://www.opendigitalradio.org
# Licence: The MIT License, see notice at the end of this file
import datetime
import logging
import os
try:
logging_path = os.path.dirname(logging.getLoggerClass().root.handlers[0].baseFilename)
except AttributeError:
logging_path = None
import numpy as np
from scipy import optimize
import matplotlib.pyplot as plt
def gen_omega(length):
if (length % 2) == 1:
raise ValueError("Needs an even length array.")
halflength = int(length / 2)
factor = 2.0 * np.pi / length
omega = np.zeros(length, dtype=np.float)
for i in range(halflength):
omega[i] = factor * i
for i in range(halflength, length):
omega[i] = factor * (i - length)
return omega
def subsample_align(sig, ref_sig, plot=False):
"""Do subsample alignment for sig relative to the reference signal
ref_sig. The delay between the two must be less than sample
Returns the aligned signal"""
n = len(sig)
if (n % 2) == 1:
raise ValueError("Needs an even length signal.")
halflen = int(n / 2)
fft_sig = np.fft.fft(sig)
omega = gen_omega(n)
def correlate_for_delay(tau):
# A subsample offset between two signals corresponds, in the frequency
# domain, to a linearly increasing phase shift, whose slope
# corresponds to the delay.
#
# Here, we build this phase shift in rotate_vec, and multiply it with
# our signal.
rotate_vec = np.exp(1j * tau * omega)
# zero-frequency is rotate_vec[0], so rotate_vec[N/2] is the
# bin corresponding to the [-1, 1, -1, 1, ...] time signal, which
# is both the maximum positive and negative frequency.
# I don't remember why we handle it differently.
rotate_vec[halflen] = np.cos(np.pi * tau)
corr_sig = np.fft.ifft(rotate_vec * fft_sig)
return -np.abs(np.sum(np.conj(corr_sig) * ref_sig))
optim_result = optimize.minimize_scalar(correlate_for_delay, bounds=(-1, 1), method='bounded',
options={'disp': True})
if optim_result.success:
best_tau = optim_result.x
if plot and logging_path is not None:
corr = np.vectorize(correlate_for_delay)
ixs = np.linspace(-1, 1, 100)
taus = corr(ixs)
dt = datetime.datetime.now().isoformat()
tau_path = (logging_path + "/" + dt + "_tau.svg")
plt.plot(ixs, taus)
plt.title("Subsample correlation, minimum is best: {}".format(best_tau))
plt.savefig(tau_path)
plt.close()
# Prepare rotate_vec = fft_sig with rotated phase
rotate_vec = np.exp(1j * best_tau * omega)
rotate_vec[halflen] = np.cos(np.pi * best_tau)
return np.fft.ifft(rotate_vec * fft_sig).astype(np.complex64)
else:
# print("Could not optimize: " + optim_result.message)
return np.zeros(0, dtype=np.complex64)
# The MIT License (MIT)
#
# Copyright (c) 2017 Andreas Steger
#
# 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.
|
