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"""
Discrete Fourier Transforms - helper.py
"""
# Created by Pearu Peterson, September 2002
__all__ = ['fftshift','ifftshift','fftfreq','rfftfreq']
from scipy_base import asarray, concatenate, arange, take, array
import types
def fftshift(x,axes=None):
""" fftshift(x, axes=None) -> y
Shift zero-frequency component to center of spectrum.
This function swaps half-spaces for all axes listed (defaults to all).
Notes:
If len(x) is even then the Nyquist component is y[0].
"""
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):
""" ifftshift(x,axes=None) - > y
Inverse of 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):
""" fftfreq(n, d=1.0) -> f
DFT 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
"""
assert isinstance(n,types.IntType)
k = range(0,(n-1)/2+1)+range(-(n/2),0)
return array(k,'d')/(n*d)
def rfftfreq(n,d=1.0):
""" rfftfreq(n, d=1.0) -> f
DFT sample frequencies (for usage with rfft,irfft).
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 = [0,1,1,2,2,...,n/2-1,n/2-1,n/2]/(d*n) if n is even
f = [0,1,1,2,2,...,n/2-1,n/2-1,n/2,n/2]/(d*n) if n is odd
"""
assert isinstance(n,types.IntType)
return array(range(1,n+1),'i')/2/float(n*d)
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