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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