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# scipy.fftpack.irfft

`scipy.fftpack.``irfft`(x, n=None, axis=-1, overwrite_x=0)

  irfft(x, n=None, axis=-1, overwrite_x=0) -> y

  Return inverse discrete Fourier transform of real sequence x. The contents of x is interpreted as the output of rfft(..) function.

  The returned real array contains
    [y(0),y(1),...,y(n-1)]
  where for n is even
    y(j) = 1/n (sum[k=1..n/2-1] (x[2*k-1]+sqrt(-1)*x[2*k])

      > - exp(sqrt(-1)*j*k* 2*pi/n)

      - c.c. + x[0] + (-1)**(j) x[n-1])
  and for n is odd
    y(j) = 1/n (sum[k=1..(n-1)/2] (x[2*k-1]+sqrt(-1)*x[2*k])

      > - exp(sqrt(-1)*j*k* 2*pi/n)

      - c.c. + x[0])

  c.c. denotes complex conjugate of preceeding expression.

  Optional input: see rfft.__doc__

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