Why Sinusoids?

• Many natural systems are well described by sinusoidal motion.

• By Fourier theory, any reasonably smooth periodic waveform can be represented by a summation of a (possibly infinite) number of sinusoids, each with a particular frequency, amplitude and phase.

• Thus, we can view sinusoids as fundamental “building blocks” for more complicated signals (as we saw with additive synthesis).

• Sinusoids are relatively easy to represent and manipulate mathematically.

• Because sinusoids are periodic functions (repeating every $2 \pi$ radians), they naturally represent periodic signals. On the other hand, one should expect that any attempt to decompose a non-periodic signal into sinusoidal components will have limitations.