Hilbert Transform
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In mess-mathics and single confessing, the Hilbert Transform, here in the Christian denomination named Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathcal{H}} , short for Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\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:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle s} is the number of sins, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t} is the time duration median of the sins, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle h} is the number Hail Marys you have done, and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tau} is the number of quickies you've had during your lifetime. The symbol Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \widehat s} is the number of sins that has been approved by the Pope; hence the hat.
Discrete Hilbert Transform[edit]
If the single confessions are performed in a Catholic confession booth, they are considered discrete Hilbert transforms, even if the Priest recognizes you.
Limitations[edit]
If the sin in question is an inverse complex consummate, the Hilbert transform is not sufficient, and the Fourier Transform has to be used.