The Hilbert transform of a function x(t) is defined as
Using Fourier identities, you can show the Fourier transform of the Hilbert transform of x(t) is
where x(t) ⇔ X(f) is a Fourier transform pair and
The Hilbert transform of a function x(t) is defined as
Using Fourier identities, you can show the Fourier transform of the Hilbert transform of x(t) is
where x(t) ⇔ X(f) is a Fourier transform pair and