Hilbert Transform
PrintA mathemtical transform that shifts each frequency component of the instantaneous spectrum by 90 degrees without affecting the magnitude. Can also be performed over limited frequency ranges using an analog all-pass filter. For a demonstration of the usefulness of the Hilbert Transform to detect the envelope of the signal, see envelope.
If a time signal is perceived as a rotating vector, then the length of the vector equals the envelope of the signal. The projection of the rotating vector on the X & Y axes then are its real and imaginary components, where we normally are only used to seeing the real part on an oscilloscope. However, using simple geometry, we know that the there real and imaginary components of a signal are related by a 90 degree phase angle, and this is basically what the Hilbert Transform does for us. Thus, for a pure sine wave, the Hilbert transform will generate a pure cosine wave, and the resulting vector as a constant magnitude, i.e. it becomes a ripple-free detector.
The Hilbert Transform is built into LabVIEW. Click demo to interactively use the Hilbert transform to find the envelope of a signal. (Requires the LabVIEW Player.)
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