[sdiy] Screwing with Square Waves

[Donald Tillman]

On Nov 1, 2013, at 12:05 PM, cheater00 . <cheater00 at gmail.com> wrote:

> On Fri, Nov 1, 2013 at 5:28 PM, Donald Tillman <don at till.com> wrote:
>> We're summing an infinite number of sines, and each is at a strength of (1/i), inversely proportional to its frequency.  If this was a (1/(i^2)) series, like a Triangle Wave, that converges.  But a (1/i) series does not mathematically converge.
> 
> A correction has to be made. Obviously the series converges, because
> there is a limit, and we know it.

We must be talking about different things... The Harmonic Series does not converge.  I was referring to that.  Which series are you referring to?

> More technically, it converges
> because there is such a function such that the absolute area between
> that function and a partial sum of our series converges to 0 as the
> number of terms of the partial series increases:
> 
> E.f(x) => Int (Sum_{n=0}^k f_n(x) - f(x)) dx -> 0, as k->+oo

I don't know what you mean here.  What exactly is f_n(x)?

> 
>> So that infinite energy has to go somewhere.
>> And as you noted, we see that energy in infinite slopes or infinite spikes.
> 
> The reference to infinite energy is better put in more technical
> terms.

I was using the word "energy" in a completely nontechnical way.  Better to refer to it as the contribution from each harmonic.

  -- Don

--
Don Tillman
Palo Alto, California
don at till.com
http://www.till.com