Let m(t) denote a message signal and m̂(t) denote the Hilbert transform of m(t). Let the carrier frequency be ωc. The single-sideband (SSB) modulated signal with the upper sideband (USB) transmitted is given as
1
m(t) cos(ωct) - m̂(t) sin(ωct)
2
m̂(t) sin(ωct)
3
m(t) sin(ωct)
4
m(t) cos(ωct) + m̂(t) sin(ωct)