scipy.fftpack.tilbert¶
- scipy.fftpack.tilbert(x, h, period=None, _cache={})[source]¶
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.