[LAU] [Sort of OT] Ringing in filters

[Ken Restivo]

On Wed, May 12, 2010 at 01:19:45AM +0200, Fons Adriaensen wrote:
> On Tue, May 11, 2010 at 03:36:08PM -0700, Mark Knecht wrote:
> 
> > Actually though, as a test of an idea I had and just because I've got
> > the data here, I'm using stock market data, decomposing the data into
> > bands of energy if you will, and then summing the bands back together
> > to see how close I come to the original data. It works fairly well
> > most of the time, but stock data can have big directional moves at
> > times which appears as a big transient event. When those events
> > complete then the slower filter bands ring and cause large
> > displacements in the output.
> 
> So you want a set of filters with the following properties:
> 
> 1. each filter has a frequency response with a shape that allows
> an intuitive interpretation as a 'bandpass', i.e. a range of
> frequencies, and
> 
> 2. the sum of the filter outputs equals the original input.
> 
> This is a *hard* problem. Basically none of the classical filter
> types have these properties. There are filter sets that can do
> this but they are quite esoteric.
> 
> 'Ringing' is not really a problem here, each of the individual
> filters may ring, as long as this is cancelled by the others 
> when you add the outputs.
> 
> An FFT will provide a set of filters having property (2), but
> each filter has a sin(x)/x shape, which is not really a bandpass.
> You can 'improve' the shape by windowing, but that destroys (2).
> And anyway using an FFT like this is a 'block' operation - how
> a sample is treated depends on its position within the block.
> Windowing requires overlapping blocks, and they won't add up
> to the original input.
> 
> > I was thinking about tearing into the code for
> > something like Jamin to look at what's done there. Maybe there are
> > better examples for me to use though?
> 
> Jamin's FFT based filter is not really a filter, it's a vocoder
> being used as a filter and it has side effects. 

Wha??? Um, yuck.

I just mastered a CD using Jamin. Was that a mistake? I mastered a CD through a vocoder? Is there a better GPL tool I should have used?

> 
> Now if the purpose of the filtering is to extract 'features' of
> the data, you really don't need property (2). And given the 
> nature of stock market data, I suspect that classic audio filters
> are not the right way to extract such features. I'd have a look
> at wavelet filters for example.
> 
> Ciao,
> 
> -- 
> FA
> 
> O tu, che porte, correndo si ?
> E guerra e morte !
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