sineefit: Change sfit4 to fit to \sin instead of \cos

And adjust the period locator accordingly.
Fitting \sin is the same mathematically, it's just conceptually more
straightforward since we're locating zero crossings anyway.

src/sinefit.py

@@ -98,12 +98,12 @@ def process(data, interval, args, insert_function, final):
             continue
 
         #p.plot(arange(N), this)
-        #p.plot(arange(N), A * cos(f0/fs * 2 * pi * arange(N) + phi) + C, 'g')
+        #p.plot(arange(N), A * sin(f0/fs * 2 * pi * arange(N) + phi) + C, 'g')
 
-        # Period starts when the argument of cosine is 3*pi/2 degrees,
+        # Period starts when the argument of sine is 0 degrees,
         # so we're looking for sample number:
-        #     n = (3 * pi / 2 - phi) / (f0/fs * 2 * pi)
+        #     n = (0 - phi) / (f0/fs * 2 * pi)
-        zc_n = (3 * pi / 2 - phi) / (f0 / fs * 2 * pi)
+        zc_n = (0 - phi) / (f0 / fs * 2 * pi)
         period_n = fs/f0
 
         # Add periods to make N positive
@@ -149,9 +149,9 @@ def sfit4(data, fs):
 
     Output:
       Parameters [A, f0,  phi, C] to fit the equation
-        x[n] = A * cos(f0/fs * 2 * pi * n + phi) + C
+        x[n] = A * sin(f0/fs * 2 * pi * n + phi) + C
       where n is sample number.  Or, as a function of time:
-        x(t) = A * cos(f0 * 2 * pi * t + phi) + C
+        x(t) = A * sin(f0 * 2 * pi * t + phi) + C
 
     by Jim Paris
     (Verified to match sfit4.m)
@@ -188,12 +188,11 @@ def sfit4(data, fs):
     # if something fails with the least squares fit, etc.
     try:
         # first guess for A0, B0 using 3-parameter fit (step c)
+        s = zeros(3)
         w = 2*pi*f0
-        D = c_[cos(w*t), sin(w*t), ones(N)]
-        s = linalg.lstsq(D, data)[0]
 
-        # Now iterate 6 times (step i)
+        # Now iterate 7 times (step b, plus 6 iterations of step i)
-        for idx in range(6):
+        for idx in range(7):
             D = c_[cos(w*t), sin(w*t), ones(N),
                   -s[0] * t * sin(w*t) + s[1] * t * cos(w*t) ] # eqn B.16
             s = linalg.lstsq(D, data)[0] # eqn B.18
@@ -202,7 +201,7 @@ def sfit4(data, fs):
         ## Extract results
         A = sqrt(s[0]*s[0] + s[1]*s[1]) # eqn B.21
         f0 = w / (2*pi)
-        phi = -arctan2(s[1], s[0]) # eqn B.22
+        phi = arctan2(s[0], s[1]) # eqn B.22 (flipped for sin instead of cos)
         C = s[2]
         return (A, f0, phi, C)
     except Exception as e: