numpy.fft.fft(a, n=None, axis=1, norm=None)
[source]
Compute the onedimensional discrete Fourier Transform.
This function computes the onedimensional npoint discrete Fourier Transform (DFT) with the efficient Fast Fourier Transform (FFT) algorithm [CT].
Parameters: 


Returns: 

Raises: 

See also
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.
The DFT is defined, with the conventions used in this implementation, in the documentation for the numpy.fft
module.
[CT]  Cooley, James W., and John W. Tukey, 1965, “An algorithm for the machine calculation of complex Fourier series,” Math. Comput. 19: 297301. 
>>> np.fft.fft(np.exp(2j * np.pi * np.arange(8) / 8)) array([2.33486982e16+1.14423775e17j, 8.00000000e+001.25557246e15j, 2.33486982e16+2.33486982e16j, 0.00000000e+00+1.22464680e16j, 1.14423775e17+2.33486982e16j, 0.00000000e+00+5.20784380e16j, 1.14423775e17+1.14423775e17j, 0.00000000e+00+1.22464680e16j])
In this example, real input has an FFT which is Hermitian, i.e., symmetric in the real part and antisymmetric in the imaginary part, as described in the numpy.fft
documentation:
>>> import matplotlib.pyplot as plt >>> t = np.arange(256) >>> sp = np.fft.fft(np.sin(t)) >>> freq = np.fft.fftfreq(t.shape[1]) >>> plt.plot(freq, sp.real, freq, sp.imag) [<matplotlib.lines.Line2D object at 0x...>, <matplotlib.lines.Line2D object at 0x...>] >>> plt.show()
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https://docs.scipy.org/doc/numpy1.17.0/reference/generated/numpy.fft.fft.html