scipy tutorial - Baustatik-Info-Server

Return k-th derivative (or integral) of a periodic sequence x.
If x_j and y_j are Fourier coefficients of periodic functions x and y, respectively, then
y_j = pow(sqrt(-1)*j*2*pi/period, order) * x_j y_0 = 0 if order is not 0.
Optional input:
Notes:
SciPy Reference Guide, Release 0.8.dev
order
The order of differentiation. Default order is 1. If order is negative, then integration is carried out
under the assumption that x_0==0.
period
The assumed period of the sequence. Default is 2*pi.
If sum(x,axis=0)=0 then
diff(diff(x,k),-k)==x (within numerical accuracy)
For odd order and even len(x), the Nyquist mode is taken zero.
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
Input:
Notes:
y_j = sqrt(-1)*coth(j*h*2*pi/period) * x_j y_0 = 0
h
Defines the parameter of the Tilbert transform.
period
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.
itilbert(x, h, period=None, _cache={})
itilbert(x, h, period=2*pi) -> y
Return inverse 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)*tanh(j*h*2*pi/period) * x_j y_0 = 0
Optional input: see tilbert.__doc__
3.3. Fourier transforms (scipy.fftpack) 171