Question

In a coherent detection process, a sinusoidally modulated DSB-SC wave, s(t) = c(t)m(t)
where the carrier wave is c(t) =A_ccos(2πf_ct) and the message signal is m(t) = A_mcos(2πf_mt),
is applied to a product modulator using a locally generated sinusoid of A_c’ amplitude and is
out of phase by φ with respect to the sinusoidal carrier used in the modulation.
(a) Draw the block diagram of the coherent detection process and label the block diagram
with the information provided above accordingly.
(b) Determine the output of the product modulator, v(t).
(c) Sketch the Fourier Transform of the output signal, V(f).
(d) Identify the two sinusoidal terms in v(t) that are produced by the upper side frequency of
the DSB-SC modulated wave and the remaining two sinusoidal terms produced by the lower
side frequency.

Answer 1

Coherent/synchronous detection of DSB SC cos S (pi f_0 t t_0) SH 1 = m (t) c(t) m(t) = Am cos 2 pi font v(t) = Ac cos 2 pi f_c t v(t) = s(t) cos (2 pi f c t + theta) v(t) = m(t) A_c cos 2 pi f c t . cos (2 pi f_c t + theta) 2 cos A cos B = cos (A + B) + cos (A - B) v(t) = A_c m (t)/2 [cos (4 pi f c t + theta) + cos theta) high free v_0(t) = A (m + 1)/2 cos theta m(t) FT m(f) A m cos 2 pi font v_0 (t) = A/2 (m + t) cos theta FT v(t) = s(t) cos (2 pi f_c + theta) = s(t) [cos 2 pi f c + cos theta - sin 2 pi f c + sin theta]