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# scipy.fftpack.ifft

scipy.fftpack.ifft(x, n=None, axis=-1, overwrite_x=False)

  Return discrete inverse Fourier transform of real or complex sequence.

  The returned complex array contains `y(0), y(1),..., y(n-1)`, where

  `y(j) = (x * exp(2*pi*sqrt(-1)*j*np.arange(n)/n)).mean()`.

  Parameters:
    x array_like

      Transformed data to invert.

    n int, optional

      Length of the inverse Fourier transform. If `n < x.shape[axis]`, x is truncated. If `n > x.shape[axis]`, x is zero-padded. The default results in `n = x.shape[axis]`.

    axis int, optional

      Axis along which the ifft’s are computed; the default is over the last axis (i.e., `axis=-1`).

    overwrite_x bool, optional

      If True, the contents of x can be destroyed; the default is False.

  Returns:
    ifft ndarray of floats

      The inverse discrete Fourier transform.

  See also

  `fft`

    Forward FFT

  Notes

  Both single and double precision routines are implemented. Half precision inputs will be converted to single precision. Non-floating-point inputs will be converted to double precision. Long-double precision inputs are not supported.

  This function is most efficient when n is a power of two, and least efficient when n is prime.

  If the data type of x is real, a “real IFFT” algorithm is automatically used, which roughly halves the computation time.

  Examples

      >>> from scipy.fftpack import fft, ifft
      >>> import numpy as np
      >>> x = np.arange(5)
      >>> np.allclose(ifft(fft(x)), x, atol=1e-15)  # within numerical accuracy.
      True