`scipy.fftpack._pseudo_diffs:tilbert`

Signature

def tilbert(x, h, period = None, _cache = <_thread._local object at 0x0000>)

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

x : array_like: The input array to transform.
h : float: Defines the parameter of the Tilbert transform.
period : float, optional: The assumed period of the sequence. Default period is 2*pi.

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.