Wavelet analysis is a relatively new method of signal processing. While one traditional method of signal processing, Fourier analysis, answers the question "what frequencies are present in a signal", wavelet analysis answers the question "what frequencies are present in a signal and where are they?" For example, human brains produce electrical fluctuations in the 8-13 Hz range (alpha waves) when the subject is relaxed and produce waves in the 13-30 Hz range (beta waves) when the subject is alert. With Fourier analysis, a professor could tell, from the brain waves of the students, whether the students fell asleep during lecture. With wavelet analysis, the professor could tell not only if the students fell asleep, but at what point in the lecture they did so. In this talk I will present an extremely simple form of wavelet processing with applications to the compression, filtering, and feature recognition of signals. This talk will be a true introduction to wavelets. No familiarity with Fourier analysis is assumed or needed-most of the mathematics that will be presented here should be accessible to a high school student. And don't worry - I won't be monitoring your brain waves!