scipy.fftpack.sc_diff

scipy.fftpack.sc_diff(x, a, b, period=None, _cache={})

Return (a,b)-sinh/cosh pseudo-derivative 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)*sinh(j*a*2*pi/period)/cosh(j*b*2*pi/period) * x_j
y_0 = 0

Parameters :

x : array_like

Input array.

a,b : float

Defines the parameters of the sinh/cosh pseudo-differential operator.

period : float, optional

The period of the sequence x. Default is 2*pi.

Notes

sc_diff(cs_diff(x,a,b),b,a) == x For even len(x), the Nyquist mode of x is taken as zero.