cupyx.scipy.signal.hilbert#

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

Compute the analytic signal, using the Hilbert transform.

The transformation is done along the last axis by default.

Parameters:

x (ndarray) – Signal data. Must be real.
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 – Analytic signal of x, of each 1-D array along axis

Return type:

ndarray

Notes

The analytic signal x_a(t) of signal 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. [1]

In other words, the negative half of the frequency spectrum is zeroed out, turning the real-valued signal into a complex signal. The Hilbert transformed signal can be obtained from np.imag(hilbert(x)), and the original signal from np.real(hilbert(x)).

References