Solution
= Solution
Using the convention adopted here, the <Hilbert transform> is
$$
\boxed{
Hf(y)=\frac1\pi\operatorname{PV}
\int_{-\infty}^{\infty}\frac{f(x)}{y-x}\,dx}.
$$
The convention with denominator $x-y$ differs by a minus sign.
= Solution
Using the convention adopted here, the <Hilbert transform> is
$$
\boxed{
Hf(y)=\frac1\pi\operatorname{PV}
\int_{-\infty}^{\infty}\frac{f(x)}{y-x}\,dx}.
$$
The convention with denominator $x-y$ differs by a minus sign.