Let the signal produced by SSB-SC modulator is S(t), a Band pass signal
, where
is In-Phase component of S(t) obtained by
i. Multiplying S(t) with .
ii. and passing the product through a LPF with suitable cut-off frequency.
By finding the Fourier Transform of in-phase component
after restricting the signal between
Similarly is the quadrature phase component of s(t), obtained by multiplying S(t) with
and by passing the resultant signal through a LPF .
By finding the Fourier Transform of Q-phase component
after restricting the signal between
Now Let’s assume S(f) is the required frequency spectrum of SSB-SC signal when only USB has been transmitted.
i.e,
from the above figure,
one can obtain ,
by shifting the signal S(f) towards right by
and left by
Now by adding and
from the above figure, results to be
from the frequency spectrum of , the time-domain representation turns out to be
Similarly,
The resultant signals and
from the frequency spectrum of turns out to be
since Signum function is
when expressed in terms of Signum function
By using Hilbert transform of m(t) , the time-domain representation turns out to be
From EQN’s (I) and (II) , the time-domain representation of SSB-SC signal results
.
similarly, SSB signal when only LSB has been transmitted
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