BirdSongToolbox.preprocess.hilbert_module

BirdSongToolbox.preprocess.hilbert_module(neural_data, output: str, smooth=False)

Use the Hilbert Transform to get either the Amplitude or Phase of the Input Neural Data

Parameters

neural_datandarray | shape (…, Samples)

Input Neural Activity during all Trials

outputstr

String that instructs what information to extract from the analytical signal, options: ‘phase’, ‘amplitude’

smoothbool, optional

If True the instantaneous phase will be passed through a sine function, defaults to False

Returns

hilbert_results: ndarray | shape (…, Samples)

Depending on the output parameter:

‘phase’: Instantaneous Phase of the Input Neural Activity in radians ‘amplitude’: Envelope (Amplitude) of the Input Neural Activity

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)).