[sdiy] Waveform analysis into non-sine components

[Rainer Buchty]

On Tue, 10 Apr 2012, David G Dixon wrote:

> ...well, yeah.  Math(s) is(are) a language, and, like any other 
> language, one must have a certain fluency before anything written in 
> that language makes sense.  Either gain the necessary fluency, or stop 
> trying to read the language.

Reminds me of good old freshmen times, where our calculus professor told 
us that we "first need to develop a common language", flooding us with 
all sorts of axioms, lemmata, and whatnot.

What he forgot, however, was telling us what to use it for -- and he 
kept it at that level for 2 semesters. Hadn't I also bought some books 
on Engineering Maths, I wouldn't have known *why* he's torturing us with 
that stuff.

And that's probably what people might refer to as "academic maths", 
i.e., presenting maths for what appears to be "maths for the purpose of 
itself".

For instance, to me the FFT explanation in Wikipedia (and plenty of 
other pages on that topic) are prime examples of what Tom dubbed 
"academic maths". You have an idea what the FFT does and want to know 
about its innards, how to implement it, get to know more. So you stumble 
across

http://en.wikipedia.org/wiki/Cooley%E2%80%93Tukey_FFT_algorithm

Mathematically speaking, this is a perfectly fine and compact 
representation. But it probably won't help anyone who, as you say, isn't 
fluent in maths as a language (and remembers some basic 
signal-processing knowledge) as the content first needs to be 
retranslated into layman's terms.

A different, IMO much more digestible approach is presented here:

 	http://fftguru.com/

Why? Because it never forgets the "why" and "how" and therefore doesn't 
lose the mathematically lesser-inclined reader within the first two 
lines.

If course, he also needs more space.

Rainer