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""" 

Discrete Fourier Transforms - helper.py 

 

""" 

from numpy.compat import integer_types 

from numpy.core import integer, empty, arange, asarray, roll 

from numpy.core.overrides import array_function_dispatch, set_module 

 

# Created by Pearu Peterson, September 2002 

 

__all__ = ['fftshift', 'ifftshift', 'fftfreq', 'rfftfreq'] 

 

integer_types = integer_types + (integer,) 

 

 

def _fftshift_dispatcher(x, axes=None): 

return (x,) 

 

 

@array_function_dispatch(_fftshift_dispatcher, module='numpy.fft') 

def fftshift(x, axes=None): 

""" 

Shift the zero-frequency component to the center of the spectrum. 

 

This function swaps half-spaces for all axes listed (defaults to all). 

Note that ``y[0]`` is the Nyquist component only if ``len(x)`` is even. 

 

Parameters 

---------- 

x : array_like 

Input array. 

axes : int or shape tuple, optional 

Axes over which to shift. Default is None, which shifts all axes. 

 

Returns 

------- 

y : ndarray 

The shifted array. 

 

See Also 

-------- 

ifftshift : The inverse of `fftshift`. 

 

Examples 

-------- 

>>> freqs = np.fft.fftfreq(10, 0.1) 

>>> freqs 

array([ 0., 1., 2., ..., -3., -2., -1.]) 

>>> np.fft.fftshift(freqs) 

array([-5., -4., -3., -2., -1., 0., 1., 2., 3., 4.]) 

 

Shift the zero-frequency component only along the second axis: 

 

>>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3) 

>>> freqs 

array([[ 0., 1., 2.], 

[ 3., 4., -4.], 

[-3., -2., -1.]]) 

>>> np.fft.fftshift(freqs, axes=(1,)) 

array([[ 2., 0., 1.], 

[-4., 3., 4.], 

[-1., -3., -2.]]) 

 

""" 

x = asarray(x) 

if axes is None: 

axes = tuple(range(x.ndim)) 

shift = [dim // 2 for dim in x.shape] 

elif isinstance(axes, integer_types): 

shift = x.shape[axes] // 2 

else: 

shift = [x.shape[ax] // 2 for ax in axes] 

 

return roll(x, shift, axes) 

 

 

@array_function_dispatch(_fftshift_dispatcher, module='numpy.fft') 

def ifftshift(x, axes=None): 

""" 

The inverse of `fftshift`. Although identical for even-length `x`, the 

functions differ by one sample for odd-length `x`. 

 

Parameters 

---------- 

x : array_like 

Input array. 

axes : int or shape tuple, optional 

Axes over which to calculate. Defaults to None, which shifts all axes. 

 

Returns 

------- 

y : ndarray 

The shifted array. 

 

See Also 

-------- 

fftshift : Shift zero-frequency component to the center of the spectrum. 

 

Examples 

-------- 

>>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3) 

>>> freqs 

array([[ 0., 1., 2.], 

[ 3., 4., -4.], 

[-3., -2., -1.]]) 

>>> np.fft.ifftshift(np.fft.fftshift(freqs)) 

array([[ 0., 1., 2.], 

[ 3., 4., -4.], 

[-3., -2., -1.]]) 

 

""" 

x = asarray(x) 

if axes is None: 

axes = tuple(range(x.ndim)) 

shift = [-(dim // 2) for dim in x.shape] 

elif isinstance(axes, integer_types): 

shift = -(x.shape[axes] // 2) 

else: 

shift = [-(x.shape[ax] // 2) for ax in axes] 

 

return roll(x, shift, axes) 

 

 

@set_module('numpy.fft') 

def fftfreq(n, d=1.0): 

""" 

Return the Discrete Fourier Transform sample frequencies. 

 

The returned float array `f` contains the frequency bin centers in cycles 

per unit of the sample spacing (with zero at the start). For instance, if 

the sample spacing is in seconds, then the frequency unit is cycles/second. 

 

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, optional 

Sample spacing (inverse of the sampling rate). Defaults to 1. 

 

Returns 

------- 

f : ndarray 

Array of length `n` containing the sample frequencies. 

 

Examples 

-------- 

>>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5], dtype=float) 

>>> fourier = np.fft.fft(signal) 

>>> n = signal.size 

>>> timestep = 0.1 

>>> freq = np.fft.fftfreq(n, d=timestep) 

>>> freq 

array([ 0. , 1.25, 2.5 , ..., -3.75, -2.5 , -1.25]) 

 

""" 

if not isinstance(n, integer_types): 

raise ValueError("n should be an 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 

 

 

@set_module('numpy.fft') 

def rfftfreq(n, d=1.0): 

""" 

Return the Discrete Fourier Transform sample frequencies 

(for usage with rfft, irfft). 

 

The returned float array `f` contains the frequency bin centers in cycles 

per unit of the sample spacing (with zero at the start). For instance, if 

the sample spacing is in seconds, then the frequency unit is cycles/second. 

 

Given a window length `n` and a sample spacing `d`:: 

 

f = [0, 1, ..., n/2-1, n/2] / (d*n) if n is even 

f = [0, 1, ..., (n-1)/2-1, (n-1)/2] / (d*n) if n is odd 

 

Unlike `fftfreq` (but like `scipy.fftpack.rfftfreq`) 

the Nyquist frequency component is considered to be positive. 

 

Parameters 

---------- 

n : int 

Window length. 

d : scalar, optional 

Sample spacing (inverse of the sampling rate). Defaults to 1. 

 

Returns 

------- 

f : ndarray 

Array of length ``n//2 + 1`` containing the sample frequencies. 

 

Examples 

-------- 

>>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5, -3, 4], dtype=float) 

>>> fourier = np.fft.rfft(signal) 

>>> n = signal.size 

>>> sample_rate = 100 

>>> freq = np.fft.fftfreq(n, d=1./sample_rate) 

>>> freq 

array([ 0., 10., 20., ..., -30., -20., -10.]) 

>>> freq = np.fft.rfftfreq(n, d=1./sample_rate) 

>>> freq 

array([ 0., 10., 20., 30., 40., 50.]) 

 

""" 

if not isinstance(n, integer_types): 

raise ValueError("n should be an integer") 

val = 1.0/(n*d) 

N = n//2 + 1 

results = arange(0, N, dtype=int) 

return results * val