DRAWING WITH FOURIER TRANSFORMS
WHAT IS THE FOURIER TRANSFORM
The Fourier Transform is a powerful mathematical and analytical tool developed by Joseph Fourier to model and study heat flow. It essentially breaks down any function into an approximation of sums of multiple sinusoids. In reality no signal is a perfect sin wave, which makes this tool extremely useful in signal processing. Variations of the Fourier Transform are found in places ranging from autotune to image processing. Its importance in the modern day relies on its ability to break down any signal and make it easy to understand, alter or store for a computer.
I’m not the most qualified to explain how it works or do justice to its true versatility and utility, so I suggest watching this video first as an introduction to the matter if you want to delve into the mathematics of it.
**PLEASE VIEW THIS ON A COMPUTER**
Below is a javascript program that I wrote to show how the transform can be used to interpret any signal as its input. Think of each circle to be rotating along the circumference of the larger one and smallest one has a pen that’s tracing out the path. The program can then draw whatever it is given, only changing the radius and number of the circles by breaking down the signal using a discrete Fourier transform.
To use the program just hold down your mouse over the black area and draw whatever you want. Release the mouse when you finish drawing. (Once you draw something you cannot redraw or add anything so refresh the program to make a new drawing).
Note : Instead of using a single complex input, I chose to use two different sets of epicycles to show what is going on, but the overall concept is still the same, with one set representing the real values and one representing the complex values.
See Also
But what is a Fourier series? From heat flow to drawing with circles | DE4 | 3 Blue 1 Brown (https://www.youtube.com/watch?v=r6sGWTCMz2k)
