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HilbertTransform Class

Discrete Hilbert Transformation.
Inheritance Hierarchy

Namespace:  Accord.Math
Assembly:  Accord.Math (in Accord.Math.dll) Version: 3.8.0
public static class HilbertTransform
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The discrete Hilbert transform is a transformation operating on the time domain. It performs a 90 degree phase shift, shifting positive frequencies by +90 degrees and negative frequencies by -90 degrees. It is useful to create analytic representation of signals.

The Hilbert transform can be implemented efficiently by using the Fast Fourier Transform. After transforming a signal from the time-domain to the frequency domain, one can zero its negative frequency components and revert the signal back to obtain the phase shifting.

By applying the Hilbert transform to a signal twice, the negative of the original signal is recovered.


  • Marple, S.L., "Computing the discrete-time analytic signal via FFT," IEEE Transactions on Signal Processing, Vol. 47, No.9 (September 1999). Available on:
  • J. F. Culling, Online, cross-indexed dictionary of DSP terms. Available on:

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