`scipy.fftpack._pseudo_diffs:diff`

Signature

   def     diff (    x    ,    order    =  1   ,    period    =  None   ,    _cache    =  <_thread._local object at 0x0000>     )

Return kth 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.

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.

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.