use fftfreq for the frequencies

also set as property and remove ability to select value by call (can do
it by indexing now)

n.b. the frequencies returned by numpy are adimensional, on the interval
[-1/2, 1/2], so we multiply by 2 * pi.

This affects the computation of Cdelta, which now comes out as correct
when s0 = 1 (for the Morlet). See #1.

Author: aaren

wavelets/transform.py

@@ -329,33 +329,16 @@ def compute_optimal_scales(self):
         sj = s0 * 2 ** (dj * np.arange(0, J + 1))
         return sj
 
-    # TODO: use np.frompyfunc on this
-    # TODO: can we just replace it with fftfreqs?
-    def w_k(self, k=None):
+    @property
+    def w_k(self):
         """Angular frequency as a function of fourier index.
 
         If no k, returns an array of all the angular frequencies
         calculated using the length of the data.
 
         See eq5 of TC.
         """
-        dt = self.dt
-        N = self.N
-        a = 2 * np.pi / (N * dt)
-        if k is None:
-            k = np.arange(N)
-            w_k = np.arange(N) * a
-            w_k[np.where(k > N // 2)] *= -1
-        elif type(k) is np.ndarray:
-            w_k = a * k
-            w_k[np.where(k > N // 2)] *= -1
-        else:
-            w_k = a * k
-            if k <= N // 2:
-                pass
-            elif k > N // 2:
-                w_k *= -1
-        return w_k
+        return 2 * np.pi * np.fft.fftfreq(self.N, self.dt)
 
     @property
     def wavelet_transform(self):
@@ -507,7 +490,7 @@ def wavelet_transform_delta(self):
         """
         Y_0 = self.wavelet.frequency  # wavelet as f(w_k, s)
 
-        WK, S = np.meshgrid(self.w_k(), self.scales)
+        WK, S = np.meshgrid(self.w_k, self.scales)
 
         # compute Y_ over all s, w_k and sum over k
         norm = (2 * np.pi * S / self.dt) ** .5  # normalisation factor with dt=1