Well, sin and cos can’t be directly computed in general, so you’ll need an approximation method such as the Taylor series to use Fourier series.
Only if you’re trying to get a numerical point evaluation. For example, one can use Fourier series to represent complex signals in terms of sine waves, and then reproduce the sine waves with hardware to reproduce the original signal. This is how a simple synthesizer produces different kinds of tones.
I spent months with the series about a decade ago. Lived and breathed it, read every book I could find on the subject. I derived expressions for it in a few high dimensional applications and efficient solutions for its calculation. To this day, it’s really really cool seeing some of those algorithms get incorporated into libraries.
Bro…I’m an engineer who has had their fair share of math, science, and electronics/circuits/electrical engineering-specific types of classes.
I hated this thing…is it brilliant in a billion ways I couldn’t begin to explain? Absolutely. But was it a new method of torture for those whose heads can’t wrap their brains around it in ways that those like you seemingly can? Yes…very much yes.
That being said, I tip my hat to you and know that I am very jealous. Congrats, we need those like you and the contributions that come with it, so thank you. :)
OMG took me a minute to get the Taylor series is a simpler Fourier series. This is good
