>>> Take a signal, repeatedly break it up into pairs of low and high
>>> frequencies, subsample those segments, and place them back into the
>>> buffer.
>>
>> I'm not at all clear on exactly how it does that.
>
> Using a pair of filters, low pass and high pass in a bank,

Doesn't look like any kind of lowpass or highpass filter response to me. 
Looks more like it's rearranging the order of the samples or something.

> so you filter low frequencies, this becomes the first stage, which is
> downsampled by 2.
>
> Apparently, once the filters are run over it, you can downsample each of
> the filtered components. The low pass can then be filtered again How
> reducing the sample rate of the high pass data doesn't discard data I'm
> not sure, yet.

When downsampling, frequencies above the Nyquist limit get reflected to 
the other side of the Nyquist limit. Usually this means that the high 
frequencies collide with the low frequencies - but if you've already 
filtered out the low frequencies, all that happens is that the spectrum 
gets flipped upside-down. You can completely reverse this process by 
upsampling and then flipping the spectrum back the right way round 
again. QED.

>> Most transform coding methods work not by *discarding* points, but by
>> *quantinising* them according to how "important" they are deemed to be.
>> This one seems a little unusual in that respect.
>
> Right. *But* you can drop every other sample because of the Nyquist limit!

Yes. I was just pointing out that other transform codings work in a 
rather different way.

>> Apparently there's a limit to how much precision you can get in time and
>> frequency. Increasing the resolution of one necessarily decreases the
>> resolution of the other. This is apparently due to the Heisenberg
>> uncertainty principle. (Which is interesting, since I thought that
>> applies only to quantum mechanics, not to general mathematical
>> phenomena...)
>
> Interesting. It makes sense, though. Low frequencies change relatively
> little in the time domain. You can tell when it occurs, when exactly a
> peak is, but now how it changes if delta-t is less than the frequency of
> the wave.

Weird, but true. And since quantum particles ARE ALSO WAVES, you start 
to understand why this might be true...

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