# 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.