Editing Single-sideband modulation (section)

===Lower sideband===
<math>s(t)</math> can also be recovered as the real part of the complex-conjugate, <math>s_\mathrm{a}^*(t),</math> which represents the negative frequency portion of <math>S(f).</math>  When <math>f_0\,</math> is large enough that <math>S\left(f - f_0\right)</math> has no negative frequencies, the product <math>s_\mathrm{a}^*(t) \cdot e^{j2\pi f_0 t}</math> is another analytic signal, whose real part is the actual ''lower-sideband'' transmission''':'''

:<math>\begin{align}
  s_\mathrm{a}^*(t)\cdot e^{j2\pi f_0 t} &= s_\text{lsb}(t) + j \cdot \widehat s_\text{lsb}(t) \\
             \Rightarrow s_\text{lsb}(t) &= \operatorname{Re}\left\{s_\mathrm{a}^*(t) \cdot e^{j2\pi f_0 t}\right\} \\
                                         &= s(t) \cdot \cos\left(2\pi f_0 t\right) + \widehat{s}(t) \cdot \sin\left(2\pi f_0 t\right).
\end{align}</math>

The sum of the two sideband signals is:

:<math>s_\text{usb}(t) + s_\text{lsb}(t) = 2s(t) \cdot \cos\left(2\pi f_0 t\right),\,</math>

which is the classic model of suppressed-carrier [[double sideband]] AM.