Time Domain Description

In the time domain, the DSB modulated signal can be represented as a time-varying waveform that consists of two sidebands, one above and one below the carrier frequency, and a constant envelope. The mathematical expression for DSB modulation is:

s(t) = Ac[1 + m(t)] cos(2πfct)

where s(t) is the modulated signal, Ac is the amplitude of the carrier signal, m(t) is the modulating signal, fc is the carrier frequency, and cos(2πfct) is the carrier waveform.

The modulating signal m(t) is typically a low-frequency signal such as an audio or video signal. The amplitude of the carrier signal is varied in proportion to the instantaneous amplitude of the modulating signal, resulting in two sidebands that are symmetrically spaced around the carrier frequency. The bandwidth of the modulated signal is twice the bandwidth of the modulating signal, which is known as the Carson's rule.

The DSB modulated signal can also be visualized using the frequency domain representation, which shows the spectral content of the signal. In the frequency domain, the DSB signal has two identical sidebands that contain the same spectral content as the modulating signal, plus the carrier frequency. The spectral content of the modulating signal is mirrored around the carrier frequency, resulting in a bandwidth that is twice the maximum frequency of the modulating signal.