Frequency Extracting, Sound Editing and The Fourier Transform by Simon Mengzhe Xu (12JLG)
When we have multiple inputs of simple sound waves with different frequencies, it is not hard to put them
together over each other and produce music. All you need to do is to add their amplitude at the same time
together and plot it on a new pair of axis, and the resulting graph may look much more complex.
It may seem easy for talented musicians to
extract single notes from a complex Chord, it
is a lot harder to extract frequencies of waves
from the result of their superposition just by
looking at them. It feels like separating mixed
color paints from the product of mixing them.
So, how do we do it?
The general strategy is to build a mathematical machine that treats signals
with a given frequency differently from other signals.
Firstly, lets get ourselves a simple sound wave with f=3 in a finite time
period, and wrap it up around a circle. The amplitude is going to be
transformed as the distance to the centre of the circle.
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