Day 3
This morning Joe introduced us to Matt Casella; he will be running our daily meetings while Joe is out this week. We received an informational page detailing what should be contained in our abstracts (which must be completed by Monday). I have not yet begun work on my project because Lauren (the grad student I will be working with on the project) is still away at a conference with Dr. Qiao so I'm hoping to get enough detail on the project this week to be able to write an effective abstract.
Working in the lab today, I learned about Fourier Series, a method of breaking down any continuous waveform into an infinite series of only sine and cosine waves of different amplitudes and frequencies. For example a square wave with a period of Π appears like this on an amplitude vs. time plot:
But a Fourier Series can create an equation that will more accurately approximate the shape of the graph as you add more terms to the series and an infinite number of terms would exactly equal the square wave.
The way the coefficients are calculated was new to me (mostly a lot of Trig integration identities) but the concept is very similar to a Taylor or MacLaurin series in calculus.
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