Well, harrumph!

Here I had thought that everybody (outside Ivy-league math PhD's living in spendid isolation in some Montana cabin, writing environmental screeds to major US newspapers -- and a few of this math PhD's dispeptic neighbors in Montana ) knew that perfect square waves exist only in theory, due to the Gibbs' phenomenon.

I'm gonna have to write a pissy letter to the governor of Montana, complaining about the education system there. ;-) 

Seriously, to make a long story short, it takes an infinite number of sin(x) components in the Fourier series expansion of a square wave to create perfect discontinuous corners. To explain that in English, a Fourier series is a way of representing any waveform as a sum of "sin(x)" and "cosine(x)" components, and sin() and cosine() are the continuous (sine-wave) functions that we see in our 60Hz power.

Here's a Wikipedia article with all the high-tech math, but also with three really illustrative figures along the right side of the page:

http://en.wikipedia.org/wiki/Gibbs_phenomenon

Ignore all the fancy math, just pay attention to the pictures along the right side of the page titled "Approximation of square wave in"... "steps" 

Now, y'all might be thinking I'm just being some sort of geek show-off, but there's a wrench-bender point to this. Ever wonder why ignition noise is so capable of interfering with radio reception? Or for the hams here, ever wonder why audio (or crystal/mechanical) filters with really tight skirts "ring like a bell" when you set the filter as tight as you can make it?

What is at work is the Gibbs' phenomenon. For ignition noise, the ignition pulse has a very sharp edge to it's waveform -- not a perfect corner, like a perfect square wave, but enough of a sharp edge that the number of odd harmonics goes well up towards 20MHz (or above) -- and that's what you're hearing on the radio; all the odd harmonics (sin(x) components of the Fourier series) of the spark pulse required to make the sharp-edged spark impulse waveform. Adding capacitance to the spark cables (by shielding them) tends to "round off" the spark impulse waveform, giving you fewer odd harmonics that you hear in the radio.

Likewise in the ham radio filter example, when you have a really sharp filter with only a few "poles" in the passband, you get a passband with a response curve that looks like the step function made from 5 terms of the Fourier series. That "ripple" on the top edge of the positive step is what the passband response of your filter looks like. Adding more poles to the filter gives you less "ringing" in the passband.

I'll quit being a geek now. I've humped enough 120-lb bales of oat hay out of the barn today to make my back start to hurt like heck. Time for a nice glass of whiskey.