And so, I have spent an entire day constructing a filter bank.

Actually constructing a bank of filters that split a signal into several 
signals is pretty easy. Getting it so that adding those signals together 
actually yields the original signal has taken me *an entire day* to day 
right.

For the longest time, the wave kept coming out somewhat out-of-phase 
with the original. Eventually I figured out that that's because I need 
to shift the input signal in relation to the filter kernel (thus making 
it technically non-causal).

And then the signal still doesn't "quite" match the original, especially 
at low frequencies. A added another channel for very low frequencies, 
and now the signals match in shape, but not quite in amplitude.

Another hour spent fiddling with scaling factors, and I discover that if 
the 1x and 2x channels are set to half the amplitude of all the other 
channels, I get a crisp, perfect signal match. Yay, me!! :-D



...Further testing reveals that while the filter bank does split the 
signal into different parts, and adding them back together exactly 
reproduces the original signal, each channel actually contains a fairly 
wide collection of frequencies. For example, the 64x channel still 
contains entirely too many high frequencies.

Damnit! >_<

I hypothesize that this is due to spectural leakage caused by the 
rectangular window over the filter kernels. Maybe with a Blackman window 
or something I can get channels that actually contain only certain 
frequencies.

Hmm, and how much do you want to bet that as soon as I change the 
details of my filter bank, the signal reconstruction will stop working 
again?

I can't help feeling that somebody somewhere has already figured all 
this stuff out, and if I could just get my hands on that information, 
all of this stuff would suddenly seem a whole lot easier... :-(

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