From 90dd3e55f043c34d447f4288d81f3fc6dccc7473 Mon Sep 17 00:00:00 2001
From: Roman Zeyde <roman.zeyde@gmail.com>
Date: Mon, 16 Feb 2015 19:11:19 +0200
Subject: [PATCH] detect: find actual starting offset of the carrier

---
 amodem/detect.py     | 28 +++++++++++++++++++---------
 tests/test_detect.py |  4 ++--
 2 files changed, 21 insertions(+), 11 deletions(-)

diff --git a/amodem/detect.py b/amodem/detect.py
index f15643c..5adfb5b 100644
--- a/amodem/detect.py
+++ b/amodem/detect.py
@@ -66,7 +66,7 @@ class Detector(object):
         bufs.append(np.array(trailing))
 
         buf = np.concatenate(bufs)
-        offset = self.find_start(buf, duration=self.CARRIER_DURATION)
+        offset = self.find_start(buf)
         start_time += (offset / self.Nsym - self.SEARCH_WINDOW) * self.Tsym
         log.debug('Carrier starts at %.3f ms', start_time * 1e3)
 
@@ -76,14 +76,24 @@ class Detector(object):
         amplitude, freq_err = self.estimate(buf[:prefix_length])
         return itertools.chain(buf, samples), amplitude, freq_err
 
-    def find_start(self, buf, duration):
-        filt = dsp.FIR(dsp.exp_iwt(self.omega, self.Nsym))
-        p = np.abs(list(filt(buf))) ** 2
-        p = np.cumsum(p)[self.Nsym-1:]
-        p = np.concatenate([[0], p])
-        length = (duration - 1) * self.Nsym
-        correlations = np.abs(p[length:] - p[:-length])
-        offset = np.argmax(correlations)
+    def find_start(self, buf):
+        carrier = dsp.exp_iwt(self.omega, self.Nsym)
+        carrier = np.tile(carrier, self.SEARCH_WINDOW // 4)
+        zeroes = carrier * 0.0
+        signal = np.concatenate([zeroes, carrier])
+        signal = (2 ** 0.5) * signal / dsp.norm(signal)
+
+        coeffs = []
+        for i in range(len(buf) - len(signal)):
+            b = buf[i:i+len(signal)]
+            c = 0.0
+            if dsp.norm(b):
+                c = np.abs(np.dot(b, signal)) / dsp.norm(b)
+            coeffs.append(c)
+
+        index = np.argmax(coeffs)
+        log.debug('Starting coherence: %.3f%%', coeffs[index] * 100)
+        offset = index + len(zeroes)
         return offset
 
     def estimate(self, buf, skip=5):
diff --git a/tests/test_detect.py b/tests/test_detect.py
index f6d9ad4..a0c96a4 100644
--- a/tests/test_detect.py
+++ b/tests/test_detect.py
@@ -19,7 +19,7 @@ def test_detect():
     detector = detect.Detector(config, pylab=common.Dummy())
     samples, amp, freq_err = detector.run(x)
     assert abs(1 - amp) < 1e-12
-    assert abs(freq_err) < 1e-16
+    assert abs(freq_err) < 1e-12
 
     x = np.cos(2 * np.pi * (2*config.Fc) * t)
     with pytest.raises(ValueError):
@@ -56,6 +56,6 @@ def test_find_start():
     for offset in range(32):
         bufs = [prefix, [0] * offset, carrier, postfix]
         buf = np.concatenate(bufs)
-        start = detector.find_start(buf, length)
+        start = detector.find_start(buf)
         expected = offset + len(prefix)
         assert expected == start