scipy.fftpack.cs_diff

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

Return (a,b)-cosh/sinh pseudo-derivative of a periodic sequence.

If x_j and y_j are Fourier coefficients of periodic functions x and y, respectively, then:

y_j = -sqrt(-1)*cosh(j*a*2*pi/period)/sinh(j*b*2*pi/period) * x_j
y_0 = 0

Parameters :

x : array_like

The array to take the pseudo-derivative from.

a, b : float

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

period : float, optional

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

Returns :

cs_diff : ndarray

Pseudo-derivative of periodic sequence x.

Notes

For even len(x), the Nyquist mode of x is taken as zero.