Say I've got a signal that I know is composed of periodic components. However, I'm worried that there are "spiky" events that are embedded in this signal, and potentially occurring periodically. I can't just look at the power spectrum of the signal, because the spiky event will show up across many frequencies in the power spectrum.
What kinds of methods are out there to tease apart components of a signal that can reasonably be decomposed into sine waves, from those that cannot (like a spike)?