scipy.fftpack.hilbert

scipy.fftpack.hilbert(x, _cache={})

hilbert(x) -> y

Return Hilbert transform of a periodic sequence x.

If x_j and y_j are Fourier coefficients of periodic functions x and y, respectively, then

y_j = sqrt(-1)*sign(j) * x_j y_0 = 0

Notes:

If sum(x,axis=0)==0 then

hilbert(ihilbert(x)) == x

For even len(x), the Nyquist mode of x is taken zero.