Sinusoids and Exponentials

This chapter provides an introduction to sinusoids, exponentials, complex sinusoids, and various associated terminology, such as exponential decay-time ``$t_{60}$'', in-phase and quadrature sinusoidal components, analytic signals, positive and negative frequencies, and constructive and destructive interference. The fundamental importance of sinusoids in the analysis of linear time-invariant systems is introduced. We also look at circular motion 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 $z$.