1 files changed, 74 insertions, 0 deletions
diff --git a/dpd/src/subsample_align.py b/dpd/src/subsample_align.py
new file mode 100755
index 0000000..c30af7c
--- /dev/null
+++ b/dpd/src/subsample_align.py
@@ -0,0 +1,74 @@
+import numpy as np
+from scipy import signal, optimize
+import sys
+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):
+    """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)
+
+        # TODO why do we only look at the real part? Because it's faster than
+        # a complex cross-correlation? Clarify!
+        return -np.sum(np.real(corr_sig) * np.real(ref_sig.real))
+
+    optim_result = optimize.minimize_scalar(correlate_for_delay, bounds=(-1,1), method='bounded', options={'disp': True})
+
+    if optim_result.success:
+        #print("x:")
+        #print(optim_result.x)
+
+        best_tau = optim_result.x
+
+        #print("Found subsample delay = {}".format(best_tau))
+
+        # 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)