Companion — Week 2
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In lecture 2a you heard seven instruments play middle C, and saw each one drawn as a bar plot of its harmonic magnitudes: a fingerprint. Lecture 2b gave you the formulas for the coefficients behind those bars.
This week's demo asks how you would get those bars from a recording you have just been handed, when the fundamental frequency is not given to you either. Along the way it introduces the standard way to choose numbers from data: pick the ones that make the squared error as small as possible, a least-squares fit.
- Finding an instrument's fingerprint — seven recordings, a 15-harmonic model, and the error plotted against each of the two kinds of parameter in it: the harmonic amplitudes and the fundamental frequency. Put a ball on each curve, release it, and watch where it stops.
In Week 1, Auto-fit walked downhill to find a system's weights. Here you can watch the same walk on two different kinds of parameter. The demo runs in the browser, needs no setup, and records nothing; it has sound.