DSB is a specific form of AM. The general form of DSB modulation of a message \(s(t) = \cos(\omega_{i}t)\):

\(\begin{aligned}s_{\mathrm{HF}}(t) & =\gamma s(t) \cos \left(\omega_{\mathrm{c}} t\right)=\gamma \cos \left(\omega_i t\right) \cos \left(\omega_{\mathrm{c}} t\right) \\& =\underbrace{\frac{\gamma}{2} \cos \left(\left(\omega_{\mathrm{c}}-\omega_i\right) t\right)}_{\text {lower sideband }}+\underbrace{\frac{\gamma}{2} \cos \left(\left(\omega_{\mathrm{c}}+\omega_i\right) t\right)}_{\text {upper sideband }}\end{aligned}\)