[sdiy] Screwing with Square Waves

[Neil Johnson]

Don,

Great page!  Looks like I need to read up on MathML.

You don't actually define what a square wave is.  There's some
hand-wavey "we all know what it looks like" and then you jump into
Fourier summations, which are only ever going to approximate a square
wave, and indeed have problems with discontinuities.  I think it would
it be worth properly defining it, and then talking about how
instantaneous discontinuities are impossible in the real world
(irrespective of what your fuzzbox might be doing), and how actually
what we call "square" waves should really be called "trapezoidal"
waves due to finite transitions (even if the transition takes 1fs it
is still finite and measurable, and therefore not a true square wave).

The "visible artifacts" you mention are due to the Gibbs effect, and
are a consequence of synthesizing a discontinuity with a bandlimited
set of sine waves.

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

The following video demonstrates these two points quite well:

https://www.youtube.com/watch?v=cIQ9IXSUzuM&t=1040

The section on Squariness is interesting.  The square waves you
generate can all be easily generated using Walsh functions. If you
want a play then I have a couple of online tools for playing with
Walsh functions (you'll need to install the Tcl plugin, or download
the source and run locally):

http://www.milton.arachsys.com/nj71/index.php?menu=2&submenu=2&subsubmenu=5&page=3

Cheers,
Neil

On 31 October 2013 18:02, Donald Tillman <don at till.com> wrote:
> Folks,
>
> Please enjoy an article I just wrote about some strange and beautiful aspects of Square Waves:
>
>     Square Wave Variations
>     http://www.till.com/articles/squares/index.html
>
> (This presentation relies heavily on the MATHML feature of modern browsers. I'm interested in hearing of any cases where it doesn't work correctly.)
>
>   -- Don
>
> --
> Don Tillman
> Palo Alto, California
> don at till.com
> http://www.till.com
>
>
>
>
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