scipy.fftpack.
tilbert#
- scipy.fftpack.tilbert(x, h, period=None, _cache=<_thread._local object>)[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:
- xarray_like
- The input array to transform. 
- hfloat
- Defines the parameter of the Tilbert transform. 
- periodfloat, optional
- The assumed period of the sequence. Default period is - 2*pi.
 
- Returns:
- tilbertndarray
- The result of the transform. 
 
 - Notes - If - sum(x, axis=0) == 0and- n = len(x)is odd, then- tilbert(itilbert(x)) == x.- If - 2 * pi * h / periodis approximately 10 or larger, then numerically- tilbert == hilbert(theoretically oo-Tilbert == Hilbert).- For even - len(x), the Nyquist mode of- xis taken zero.