scipy.fftpack.tilbert

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

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

Parameters:

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.

Returns:

tilbert : ndarray

The result of the transform.

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.