# nlcpy.fft.fft

nlcpy.fft.fft(a, n=None, axis=- 1, norm=None)[ソース]

Computes the one-dimensional discrete fourier transform.

This function computes the one-dimensional n-point discrete fourier transform (DFT) with the efficient fast fourier transform (FFT) algorithm.

Parameters
aarray_like

Input array, can be complex.

nint,optional

Length of the transformed axis of the output. If n is smaller than the length of the input, the input is cropped. If it is larger, the input is padded with zeros. If n is not given, the length of the input along the axis specified by axis is used.

axisint,optional

Axis over which to compute the FFT. If not given, the last axis is used. If axis is larger than the last axis of a, IndexError occurs.

norm{None, "ortho"},optional

Normalization mode. By default(None), the transforms are unscaled. It norm is set to "ortho", the return values will be scaled by .

Returns
outcomplex ndarray

The truncated or zero-padded input, transformed along the axis indicated by axis , or the last one if axis is not specified.

ifft

Computes the one-dimensional inverse discrete fourier transform.

fft2

Computes the 2-dimensional discrete fourier transform.

fftn

Computes the n-dimensional discrete fourier transform.

rfftn

Computes the n-dimensional discrete fourier transform for a real array.

fftfreq

Returns the discrete fourier transform sample frequencies.

FFT (fast fourier transform) refers to a way the discrete fourier transform (DFT) can be calculated efficiently, by using symmetries in the calculated terms. The symmetry is highest when n is a power of 2, and the transform is therefore most efficient for these sizes.

Examples

>>> import nlcpy as vp
>>> vp.fft.fft(vp.exp(2j * vp.pi * vp.arange(8) / 8))
array([-3.44509285e-16+1.14423775e-17j,  8.00000000e+00-8.52069395e-16j,
2.33486982e-16+1.22464680e-16j,  0.00000000e+00+1.22464680e-16j,
9.95799250e-17+2.33486982e-16j,  0.00000000e+00+1.17281316e-16j,
1.14423775e-17+1.22464680e-16j,  0.00000000e+00+1.22464680e-16j])


In this example, real input has an FFT which is Hermitian, i.e., symmetric in the real part and anti-symmetric in the imaginary part:

>>> import matplotlib.pyplot as plt
>>> t = vp.arange(256)
>>> sp = vp.fft.fft(vp.sin(t))
>>> freq = vp.fft.fftfreq(t.shape[-1])
>>> _ = plt.plot(freq, sp.real, freq, sp.imag)
>>> plt.show()