Re: Phaeless filtering

hi guyz. i'm finally back home in the Green Mountains (actually i'm 30
meters above sea level by the Lake).

in article HLudnTGmWJVOGHffRVn-tg@xxxxxxxxxxxxxx, Fred Marshall at
fmarshallx@xxxxxxxxxxxxxxxxxxxx wrote on 07/29/2005 15:34:

> I might describe what's in that reference as follows:
>
> 1) Filter a block of data using an IIR filter.
> 2) Filter the resulting output in reverse direction through the same IIR
> filter.
> In order to do this, you need to decide when the output of the filter
> "stops" relative to the size of the input block. Otherwise, you will
> compute forever and wait forever.

this is what *truncated* IIR filters are good for. they're really are,
strictly speaking, FIR filters, but they are implemented by use of
recursion. (again, the moving average or moving sum is a good first example
of the truncated IIR.)


> Having made the decision when the output stops, you have defined a FIR
> filter that has a truncated version of the IIR filter.

but you can't just hack off samples from the output of the IIR. you need a
legit LTI implementation of this thing.

> Since there were no constraints mentioned regarding the IIR filter and
> because IIR filters don't normally have linear phase / constant delay with
> frequency, running the output in the opposite direction through the
> so-defined FIR filter is the same as running the output straight through a
> reversed version of the FIR filter EXCEPT in the first case the output is
> reversed relative to the original input. So, you might want to reverse the
> filter instead of the data.
>
> If you reverse the filter instead of the data for the second pass, then it's
> as though there are two FIR filters in series. This suggests that you might
> combine their impulse responses into a single impulse response. Assuming
> that the impulse response decays then you might want to put the reversed
> filter first, followed by the original - in order to get a more "well
> behaved" impulse response. Either way, it becomes a symmetrical FIR filter
> that has linear phase and *does* have delay in the normal way of defining
> delay.

check out that whatever paper by Avery Wang and Julius Smith about that
(must i look it up?). if you reverse the FIR as a truncated IIR, it is
theoretically stable (because you cancelled an unstable pole with a zero)
but the roundoff noise blows up.

--

r b-j rbj@xxxxxxxxxxxxxxxxxxxx

"Imagination is more important than knowledge."


.

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