We can alter the number of rotations of the circle on the new
graph to achieve different graphs, and the number of full
rotations per second if our new ‘winding frequency’. This is a
graph of f=0.5, therefore it plots the length of a wave in one
second in half of the cycle, and as we can see there is 6 peaks in
one rotation. The frequency of the sound wave is fixed, but we
can make the new winding frequency faster or slower.
When the winding frequency matches the original frequency,
some unusual pattern appears. All of the high amplitude-points
on the original graph is now all on the right side of the circle, and
the lower ones are all on the left side. So how do we use this
property of the transformation in order to make our mathematical
machine that tells us what the original frequency is?
We can plot a graph of the geometric centre (shown as blue dote)
of the graph onto a new graph of its x coordinate on the winding
graph against time. When the frequencies match, the center of math is unusually pointed to the right side
This transformation can be called the “almost Fourier Transformation. As we can see, the graph seem rather
close to the x axis all along the region which we do take date, but at the original frequency of 3 there is an
unusual peak.
Below is another graph plotted when the original frequency is 2, and a graph when f=3.
As we can see from the graph, it is now all easier to identify the frequency of a simple sound wave just by
looking at where the peak is after the two transformations.
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