# Hilbert Transform

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In mess-mathics and single confessing, the Hilbert Transform, here in the Christian denomination named $\displaystyle \mathcal{H}$ , short for $\displaystyle \mathcal{H}$ oly Mother of God, is obtained by confessing single sins to the Minister or Priest. Though not strictly a Christian process, it does however require you to believe in Jesus Christ as your personal savior. The Hilbert transform was developed by the late Reverend Scott Adams as an alternative to being bored.

The Hilbert transform is given by:

$\displaystyle \widehat s(t) = \mathcal{H}\{s\}(t) = (h*s)(t) = \frac{1}{\pi}\int_{-\infty}^{\infty}\frac{s(\tau)}{t-\tau}\, d\tau.\,$

where $\displaystyle s$ is the number of sins, $\displaystyle t$ is the time duration median of the sins, $\displaystyle h$ is the number Hail Marys you have done, and $\displaystyle \tau$ is the number of quickies you've had during your lifetime. The symbol $\displaystyle \widehat s$ is the number of sins that has been approved by the Pope; hence the hat.

## Discrete Hilbert Transform

If the single confessions are performed in a Catholic confession booth, they are considered discrete Hilbert transforms, even if the Priest recognizes you.

## Limitations

If the sin in question is an inverse complex consummate, the Hilbert transform is not sufficient, and the Fourier Transform has to be used.