Script showing fourier transforms at arbitrary frequency,

allowing to determine the phase at any frequency without having to resort to interpolation of a DFT.

fourier/mylib/fft.py

@@ -42,3 +42,44 @@ def ft_spectrum( signal, sample_rate=1, ftfunc=None, freqfunc=None, mask_bias=Fa
     else:
         return spectrum[1:], freqs[1:]
 
+def ft_corr_vectors(freqs, time):
+    """
+    Get the cosine and sine terms for freqs at time.
+
+    Takes the outer product of freqs and time.
+    """
+    freqtime = np.outer(freqs, time)
+
+    c_k = np.cos(2*np.pi*freqtime)
+    s_k = np.sin(2*np.pi*freqtime)
+
+    return c_k, s_k
+
+def direct_fourier_transform(freqs, time, samplesets_iterable):
+    """
+    Determine the fourier transform of each sampleset in samplesets_iterable at freqs.
+
+    The samplesets are expected to have the same time vector.
+
+    Returns either a generator to return the fourier transform for each sampleset
+    if samplesets_iterable is a generator
+    or a numpy array.
+    """
+
+    c_k, s_k = ft_corr_vectors(freqs, time)
+
+    if not hasattr(samplesets_iterable, '__len__') and hasattr(samplesets_iterable, '__iter__'):
+        # samplesets_iterable is an iterator
+        # return an iterator containing (real, imag) amplitudes
+        return ( (np.dot(c_k, samples), np.dot(s_k, samples)) for samples in samplesets_iterable )
+
+    # Numpy array
+    return np.dot(c_k, samplesets_iterable), np.dot(s_k, samplesets_iterable)
+
+
+
+def discrete_fourier_properties(samples, samplerate):
+    """
+    Return f_delta and f_nyquist.
+    """
+    return (samplerate/(len(samples)), samplerate/2)