numpy.fft.helper

module documentation

Discrete Fourier Transforms - helper.py
Variable integer​_types Undocumented
Function ​_fftshift​_dispatcher Undocumented
Function fftfreq Return the Discrete Fourier Transform sample frequencies.
Function fftshift Shift the zero-frequency component to the center of the spectrum.
Function ifftshift The inverse of fftshift. Although identical for even-length x, the functions differ by one sample for odd-length x.
Function rfftfreq Return the Discrete Fourier Transform sample frequencies (for usage with rfft, irfft).
integer_types =

Undocumented

def _fftshift_dispatcher(x, axes=None):

Undocumented

@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])
@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.]])
@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.]])
@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.])