Triangle Wave using Fourier Synthesis

Thread Starter

bigdinbassett

Joined Jan 9, 2018
1
I understand a periodic waveform can be represented by an infinite sum of sinusoids. I'm having a hard time understanding why the phase of every other odd harmonic changes signs of phase shifts by 180 degrees. Why do the signs change?

Thanks!
 

MrAl

Joined Jun 17, 2014
11,396
I understand a periodic waveform can be represented by an infinite sum of sinusoids. I'm having a hard time understanding why the phase of every other odd harmonic changes signs of phase shifts by 180 degrees. Why do the signs change?

Thanks!
Hi,

I havent checked your particular triangle wave and you could post that, but if that is true that the signs change then that's just the way it goes. If that is what it takes, that's what it takes to reconstruct the original wave.
It's like curve fitting, where you get a set of coefficients and those coefficients pop out from the solution simply because that is what it takes to reconstruct the wave.
If you want to see more, try changing one, two, or all of the signs and see what wave you get then. It will be a different wave. That's the way it works because equations for waves require circuit coeffcieints no matter what type of equation you have.

Even this:
z=2*x-3*y

certainly wont be the same as:
z=2*x+3*y

simply because it's a different equation once you change that one sign.

As another more interesting example, consider the series:
sum x^n/n! for n=0 to infinity (or just to n=23 for example)
then evaluate with x=1. We get the constant 'e'=2.71...
Now change every other term to be negative:
sum (-1)^n*x^n/n! for n=0 to 23
and again evaluate with x=1, we now get 1/e=1/2.71...

So changing every other term in that series led to the reciprocal constant when we evaluated it with x being some constant like 1.
So just like most other equations or sums this one changed a lot when we change some signs.
 
Last edited:
Top