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# scipy.fftpack.diff

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

  diff(x, order=1, period=2*pi) -> y

  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.

  Optional input:
    order
      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
      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.

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