scipy.fftpack.tilbert

scipy.fftpack.tilbert(x, h, period=None, _cache={})

tilbert(x, h, period=2*pi) -> y

Return h-Tilbert 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)*coth(j*h*2*pi/period) * x_j y_0 = 0

Input:

h

Defines the parameter of the Tilbert transform.

period

The assumed period of the sequence. Default period is 2*pi.

Notes:

If sum(x,axis=0)==0 and n=len(x) is odd then

tilbert(itilbert(x)) == x

If 2*pi*h/period is approximately 10 or larger then numerically

tilbert == hilbert

(theoretically oo-Tilbert == Hilbert). For even len(x), the Nyquist mode of x is taken zero.