In this problem we derive Equation that defines the frequency response H_Q (?) of the filter that operates on the message signal m (t) to produce m` (t) for VSB modulation. The signal m` (t), except for a scaling factor, constitutes the quadrature components of s (t), to do the derivation, we apply s (t) to the coherent of Figure so as to recover a scaled version of the original message signal m (t).

(a) Starting with the block diagram of Figure for the generation of VSB modulated wave, determine the Fourier transform V (?) of the product modulator output v (t) in Figure in term of the Fourier transform of the message signal m (t) and the frequency response H (?) of the band-pass filter Figure.

(b) Hence, by evaluating the Fourier transform of the low-pass filter output in Figure, determine the condition that must be satisfied by H_Q (?) in terms of H (? to assure perfect recovery of the original message signal m (t), except for a scaling factor.

Output signal representing a scaled version of the message signal m(t) Product modulator Low-pass tilter VSB modulated signal s(1) A, cos (2f,0