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"""
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)
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