scipy.fftpack.diff¶
-
scipy.fftpack.
diff
(x, order=1, period=None, _cache={})[source]¶ 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
- xarray_like
Input array.
- orderint, 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
.- periodfloat, optional
The assumed period of the sequence. Default is
2*pi
.
Notes
If
sum(x, axis=0) = 0
thendiff(diff(x, k), -k) == x
(within numerical accuracy).For odd order and even
len(x)
, the Nyquist mode is taken zero.