Show that the output yt contains a frequency component at

Question

The modulated signal in an SSB-SC Modulation system is given by

Φ_SSB(t) = m(t) cos2Πf_ct ± m^ (t) sin 2Πf_ct

where f_c is the carrier frequency, the ± sign indicates whether the modulated signal is LSB or USB, and m^(t) denotes the Hilbert transform of m(t).

The modulated signal is applied to a square-law device characterized by

y(t) = x²(t)

Show that the output y(t) contains a frequency component at twice the carrier frequency but it has a tune-varying phase. which makes it impractical to recover the carrier by squaring.