Formula: Hilbert transform
\(cos (2 \pi f_0t)\) \(\xrightarrow{\text{TH}}\) \(sin (2 \pi f_0t)\)
\(sin (2 \pi f_0t)\) \(\xrightarrow{\text{TH}}\) \(cos (2 \pi f_0t)\)
\(\frac{\sin{\left(t\right)}}{t}\) \(\xrightarrow{\text{TH}}\) \(\frac{\left[1-\cos(t)\right]}{t}\)
\(\frac{1}{t^2}\)\(\xrightarrow{\text{TH}}\) \(\frac{1}{{(1+t}^2)}\)
\(exp\left(-\propto\left|t\right|\right)cos\left(2\pi f_0t\right)\)\(\xrightarrow{\text{TH}}\) \(exp\left(-\propto\left|t\right|\right)sin\left(2\pi f_0t\right)\)