Use linear regression in sigproc

sigproc.py

@@ -101,11 +101,11 @@ def extract_symbols(x, freq, offset=0):
         yield np.dot(Hc, symbol)
 
 
-def drift(S):
-    x = np.arange(len(S))
-    x = x - np.mean(x)
-    y = np.unwrap(np.angle(S)) / (2*np.pi)
-    mean_y = np.mean(y)
-    y = y - mean_y
-    a = np.dot(x, y) / np.dot(x, x)
-    return a, mean_y
+def linear_regression(x, y):
+    ''' Find (a,b) such that y = a*x + b. '''
+    x = np.array(x)
+    y = np.array(y)
+    ones = np.ones(len(x))
+    M = np.array([x, ones]).T
+    a, b = linalg.lstsq(M, y)[0]
+    return a, b

test_sigproc.py

@@ -1,12 +1,12 @@
 import sigproc
 import itertools
-import common
+import config
 import numpy as np
 import random
 
 
 def test_qam():
-    q = sigproc.QAM(common.symbols)
+    q = sigproc.QAM(config.symbols)
     r = random.Random(0)
     m = q.bits_per_symbol
     bits = [tuple(r.randint(0, 1) for j in range(m)) for i in range(1024)]
@@ -16,12 +16,10 @@ def test_qam():
     assert decoded == bits
 
 
-def test_drift():
-    fc = 10e3
-    df = 1.23
-    f = fc + df
-    x = np.cos(2 * np.pi * f / common.Fs * np.arange(common.Fs))
-    S = sigproc.extract_symbols(x, fc)
-    S = np.array(list(S))
-    df_ = sigproc.drift(S) / common.Tsym
-    assert abs(df - df_) < 1e-5, (df, df_)
+def test_linreg():
+    x = np.array([1, 3, 2, 8, 4, 6, 9, 7, 0, 5])
+    a, b = 12.3, 4.56
+    y = a * x + b
+    a_, b_ = sigproc.linear_regression(x, y)
+    assert abs(a - a_) < 1e-10
+    assert abs(b - b_) < 1e-10