Compute the analytic signal, using the Hilbert transform.
The transformation is done along the last axis by default.
Parameters: | x : array_like
N : int, optional
axis : int, optional
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Returns: | xa : ndarray
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Notes
The analytic signal x_a(t) of signal x(t) is:
where F is the Fourier transform, U the unit step function, and y the Hilbert transform of x. [R136]
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
[R136] | (1, 2) Wikipedia, “Analytic signal”. http://en.wikipedia.org/wiki/Analytic_signal |