Jarhyn
Wizard
- Joined
- Mar 29, 2010
- Messages
- 15,596
- Gender
- Androgyne; they/them
- Basic Beliefs
- Natural Philosophy, Game Theoretic Ethicist
That's the thing though... The triangle wave is the arcsin of the sin.Jarhyn,
As long as you are enjoying yourself I think hat is all that really matters.
As to triangle waves and Fourier series.
Put a sine wave into an audio amp and you hear a single tone. Combine two sines and you hear a sound. Put the combined signal through a filter that rejects one of the sines and you hear only a single tone.
A square or triangle wave has a series that describes the single sines that make up the signal. Put a triangle wave trough a bandpass filter that selects one of the sines in its Fourier series and you hear the frequency.
Put a square wave with a frequency of 1kz through a low pass filter that cuts off above 1kz and you get a 1kz sine wave.
Anyway, I discussed the whole thing with a coworker who has his master's in math, and physics too, I think?
He managed to follow along with it as I put it all together for him, and we came out of it both agreeing that finding the fourier series of tanh sums is a worthwhile endeavor because they're "smooth" in a way that the absolute value version is not, and smoothness is one of my goals as to how to improve the result.