Invisible <voi### [at] devnull> wrote:
> 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... :-(

  Sorry for quoting the entire long post, but I find it rather amusing
that this amount of text doesn't really tell exactly *what* you are doing.

  The only thing the text refers to is some completely unspecified "signal",
as well as a completely unspecified "wave".

  What "signal"? Radio signal? TV signal? Sound signal? Video signal?
Something completely different? What is the source of this signal? What
is it that you are trying to do with this "filter" you are applying to this
"signal"? What is the point of your post anyways?

-- 
                                                          - Warp

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