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# scipy.fftpack.diff

`scipy.fftpack.``diff`(x, order=1, period=None, _cache={})

  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.

  Parameters: | x : array_like Input array. order : int, optional 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 : float, optional The assumed period of the sequence. Default is `2*pi`.

  Notes

  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.