class function_template(): def old_fft(name, state=None): """This function does something. :param name: The name to use. :type name: str. :param state: Current state to be in. :type state: bool. :returns: int -- the return code. :raises: AttributeError, KeyError """ return 0 def fft(a, n=None, axis=-1): """ Compute 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 [CT]. Parameters ---------- a : array_like Input array, can be complex. n : int, 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. axis : int, optional Axis over which to compute the FFT. If not given, the last axis is used. Returns ------- out : complex ndarray The truncated or zero-padded input, transformed along the axis indicated by `axis`, or the last one if `axis` is not specified. Raises ------ IndexError if `axes` is larger than the last axis of `a`. See Also -------- numpy.fft : for definition of the DFT and conventions used. ifft : The inverse of `fft`. fft2 : The two-dimensional FFT. fftn : The *n*-dimensional FFT. rfftn : The *n*-dimensional FFT of real input. fftfreq : Frequency bins for given FFT parameters. Notes ----- 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. References ---------- .. [CT] Cooley, James W., and John W. Tukey, 1965, "An algorithm for the machine calculation of complex Fourier series," *Math. Comput.* 19: 297-301. Examples -------- >>> np.fft.fft(np.exp(2j * np.pi * np.arange(8) / 8)) array([ -3.44505240e-16 +1.14383329e-17j, 8.00000000e+00 -5.71092652e-15j, 2.33482938e-16 +1.22460635e-16j, 1.64863782e-15 +1.77635684e-15j, 9.95839695e-17 +2.33482938e-16j, 0.00000000e+00 +1.66837030e-15j, 1.14383329e-17 +1.22460635e-16j, -1.64863782e-15 +1.77635684e-15j]) >>> 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) [, ] >>> plt.show() 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, as described in the `numpy.fft` documentation. """ return 0