#### Previous topic

scipy.fftpack.rfft

#### Next topic

scipy.fftpack.dct

# scipy.fftpack.irfft¶

scipy.fftpack.irfft(x, n=None, axis=-1, overwrite_x=False)[source]

Return inverse discrete Fourier transform of real sequence x.

The contents of x are interpreted as the output of the rfft function.

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. irfft : ndarray of floats The inverse discrete Fourier transform.

Notes

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 + (-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)


c.c. denotes complex conjugate of preceding expression.

For details on input parameters, see rfft.