) * 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 preceding expression. For details on input parameters, see `rfft`. To process (conjugate-symmetric) frequency-domain data with a complex datatype, consider using the newer function `scipy.fft.irfft`. Examples -------- >>> from scipy.fftpack import rfft, irfft >>> a = [1.0, 2.0, 3.0, 4.0, 5.0] >>> irfft(a) array([ 2.6 , -3.16405192, 1.24398433, -1.14955713, 1.46962473]) >>> irfft(rfft(a)) array([1., 2., 3., 4., 5.]) N)