Signals are all about us. In entertainment and education we have audio, images, and video. In science and engineering, experimental and process data are typically signals. In medicine electrocardiograms, x-rays, ultrasounds, MRIs, and CT scans are all signals. In this talk we first present a vector space model of signals with numerous examples. Next we examine how signals may be analyzed or synthesized using bases of waveforms. The bases are selected according to the application in mind. Finally, because we now have enormous signal generating and computational capacity, we can redundantly sample, analyze and synthesize signals. This leads to frames, a generalization of bases. A simple use of frames is to reconstruct a transmitted signal when part of the signal is lost.

This talk is intended for a general audience and only makes significant use of Linear Algebra.