Signaalin x ( t ) {\displaystyle x(t)} Hilbert-muunnos x ^ ( t ) {\displaystyle {\hat {x}}(t)} on
ja käänteismuutos
![{\displaystyle {\hat {x}}(t)={\mathcal {H}}[x(t)]={\frac {1}{\pi }}\int _{-\infty }^{\infty }{\frac {x(s)}{t-s}}ds}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8f98d81bee34ecab7fefefd026f29c9208cdb8c1)
![{\displaystyle x(t)={\mathcal {H}}^{-1}[{\hat {x}}(t)]={\frac {-1}{\pi }}\int _{-\infty }^{\infty }{\frac {{\hat {x}}(s)}{t-s}}ds}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8a14b8a346aa33be6f3bb479d16326c0beba710f)