Frequency Domain Description SSB-SC

The frequency domain representation of an SSB-SC signal can be illustrated using a Fourier transform. The Fourier transform of an SSB-SC signal produces a single-sideband spectrum with the upper or lower sideband present, depending on the type of SSB-SC modulation used.

The SSB-SC signal can be expressed mathematically as:

x(t) = m(t)cos(2πfct) + jw(t)sin(2πfct)

where m(t) is the message signal, fc is the carrier frequency, and w(t) is the Hilbert transform of m(t), which is used to obtain the opposite sideband.

In summary, the frequency domain description of SSB-SC modulation involves the suppression or removal of the carrier frequency and one of the sidebands, resulting in a narrowband signal with a bandwidth equal to the message bandwidth.

Consider a message signal 𝑚(𝑡) with a spectrum 𝑀(𝑓) band limited to the interval– 𝑤 < 𝑓 < 𝑤 as shown in Fig.3, the DSBSC wave obtained by multiplexing 𝑚(𝑡) by the carrier wave 𝑐(𝑡) = 𝐴𝑐cos(2𝜋𝑓𝑐 𝑡) and is also shown in figure 4. The upper side band is represented in duplicate by the frequencies above 𝑓𝑐 and those below -𝑓𝑐 , and when only upper side band is transmitted; the resulting SSB modulated wave has the spectrum shown in figure 6.

Frequency Domain Description SSB-SC