1 files changed, 111 insertions, 0 deletions
diff --git a/python/dpd/src/subsample_align.py b/python/dpd/src/subsample_align.py
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+++ b/python/dpd/src/subsample_align.py
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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.