Hilbert transform
A mathematical transform that converts a real signal into an analytic signal, constructing a one-sided-spectrum complex signal through a 90-degree phase shift. It is used to extract instantaneous amplitude and phase.
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The frequency-domain response of a real wavelet is distributed symmetrically over positive and negative frequencies, and the transform coefficients are real, so amplitude and phase cannot be separated directly; forcibly constructing an analytic signal requires post-processing such as the Hilbert transform and introduces edge effects and computational burden.
The Hilbert transform is a standard tool for converting a real signal into an analytic signal, constructing a complex signal containing only positive frequencies by shifting the positive-frequency components by -90° and the negative-frequency components by +90°.
Applying the Hilbert transform to the real wavelet transform coefficients scale by scale approximately yields analytic wavelet coefficients, from which the instantaneous amplitude and phase can then be extracted.
All Facts (3)
The frequency-domain response of a real wavelet is distributed symmetrically over positive and negative frequencies, and the transform coefficients are real, so amplitude and phase cannot be separated directly; forcibly constructing an analytic signal requires post-processing such as the Hilbert transform and introduces edge effects and computational burden.
50%UnverifiedThe Hilbert transform is a standard tool for converting a real signal into an analytic signal, constructing a complex signal containing only positive frequencies by shifting the positive-frequency components by -90° and the negative-frequency components by +90°.
50%UnverifiedApplying the Hilbert transform to the real wavelet transform coefficients scale by scale approximately yields analytic wavelet coefficients, from which the instantaneous amplitude and phase can then be extracted.
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