Sinusoids and Exponentials

This chapter provides an introduction to sinusoids, exponentials, complex sinusoids, exponential decay-time ``$t_{60}$'', in-phase and quadrature sinusoidal components, analytic signals, positive and negative frequencies, constructive and destructive interference, and sinusoids in linear time-invariant systems. We also derive that circular motion can be expressed as the vector sum of in-phase and quadrature sinusoidal motions. Both continuous and discrete-time sinusoids are considered. In particular, a sampled complex sinusoid is generated by successive powers of any complex number $z$.