scipy.signal.hilbert(x, N=None, axis=-1)[source]

Compute the analytic signal.

The transformation is done along the last axis by default.

Parameters :

x : array_like

Signal data

N : int, optional

Number of Fourier components. Default: x.shape[axis]

axis : int, optional

Axis along which to do the transformation. Default: -1.

Returns :

xa : ndarray

Analytic signal of x, of each 1-D array along axis


The analytic signal x_a(t) of x(t) is:

x_a = F^{-1}(F(x) 2U) = x + i y

where F is the Fourier transform, U the unit step function, and y the Hilbert transform of x. [R81]

axis argument is new in scipy 0.8.0.


[R81](1, 2) Wikipedia, “Analytic signal”.

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