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
andn = len(x)
is odd thentilbert(itilbert(x)) == x
.If
2 * pi * h / period
is approximately 10 or larger, then numericallytilbert == hilbert
(theoretically oo-Tilbert == Hilbert).For even
len(x)
, the Nyquist mode ofx
is taken zero.