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Diffstat (limited to 'numpy/fft/helper.py')
-rw-r--r-- | numpy/fft/helper.py | 116 |
1 files changed, 116 insertions, 0 deletions
diff --git a/numpy/fft/helper.py b/numpy/fft/helper.py new file mode 100644 index 000000000..e2e36c323 --- /dev/null +++ b/numpy/fft/helper.py @@ -0,0 +1,116 @@ +""" +Discrete Fourier Transforms - helper.py +""" +# Created by Pearu Peterson, September 2002 + +__all__ = ['fftshift','ifftshift','fftfreq'] + +from numpy.core import asarray, concatenate, arange, take, \ + integer, empty +import types + +def fftshift(x,axes=None): + """ + Shift zero-frequency component to center of spectrum. + + This function swaps half-spaces for all axes listed (defaults to all). + If len(x) is even then the Nyquist component is y[0]. + + Parameters + ---------- + x : array_like + Input array. + axes : int or shape tuple, optional + Axes over which to shift. Default is None which shifts all axes. + + See Also + -------- + ifftshift + + """ + tmp = asarray(x) + ndim = len(tmp.shape) + if axes is None: + axes = range(ndim) + y = tmp + for k in axes: + n = tmp.shape[k] + p2 = (n+1)/2 + mylist = concatenate((arange(p2,n),arange(p2))) + y = take(y,mylist,k) + return y + + +def ifftshift(x,axes=None): + """ + Inverse of fftshift. + + Parameters + ---------- + x : array_like + Input array. + axes : int or shape tuple, optional + Axes over which to calculate. Defaults to None which is over all axes. + + See Also + -------- + fftshift + + """ + tmp = asarray(x) + ndim = len(tmp.shape) + if axes is None: + axes = range(ndim) + y = tmp + for k in axes: + n = tmp.shape[k] + p2 = n-(n+1)/2 + mylist = concatenate((arange(p2,n),arange(p2))) + y = take(y,mylist,k) + return y + +def fftfreq(n,d=1.0): + """ + Discrete Fourier Transform sample frequencies. + + The returned float array contains the frequency bins in + cycles/unit (with zero at the start) given a window length `n` and a + sample spacing `d`. + :: + + f = [0,1,...,n/2-1,-n/2,...,-1]/(d*n) if n is even + f = [0,1,...,(n-1)/2,-(n-1)/2,...,-1]/(d*n) if n is odd + + Parameters + ---------- + n : int + Window length. + d : scalar + Sample spacing. + + Returns + ------- + out : ndarray, shape(`n`,) + Sample frequencies. + + Examples + -------- + >>> signal = np.array([-2., 8., -6., 4., 1., 0., 3., 5.]) + >>> fourier = np.fft.fft(signal) + >>> n = len(signal) + >>> timestep = 0.1 + >>> freq = np.fft.fftfreq(n, d=timestep) + >>> freq + array([ 0. , 1.25, 2.5 , 3.75, -5. , -3.75, -2.5 , -1.25]) + + """ + assert isinstance(n,types.IntType) or isinstance(n, integer) + val = 1.0/(n*d) + results = empty(n, int) + N = (n-1)//2 + 1 + p1 = arange(0,N,dtype=int) + results[:N] = p1 + p2 = arange(-(n//2),0,dtype=int) + results[N:] = p2 + return results * val + #return hstack((arange(0,(n-1)/2 + 1), arange(-(n/2),0))) / (n*d) |