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+# -*- 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
+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_location=None):
+ """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_location 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 = (plot_location + "/" + dt + "_tau.png")
+ 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.