DC Mathematica 2018

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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