i wrote:

> >i don'r really fiddle with issues regarding ROC and such anymore. �i
> >can't really understand how to deal with (simulate or not) an acausal
> >IIR filter with exponential components that blow up to infinity. �but
> >for an FIR, it's no problem. �if you can set aside a certain finite
> >amount of delay, you can deal with any acausal FIR fine. �and then put
> >the delay back and it's causal. �no big deal.
>
...
On Apr 23, 6:38 pm, "dszabo" <62466@dsprelated> wrote:
>
> Crazy, I wasn't even going to try thinking in terms of an acausal IIR
> filter. &#4294967295;I was thinking more in terms of the FIR coefficients converging to
> 0 as n approaches +-infinity.

and even before that.

> &#4294967295;Is an acausal IIR filter even a thing? &#4294967295;Like
> a useful thing?

no, not really.  but as i said, i haven't been fiddling around with
that ROC thing since college daze.  if i recall, you can have an
acausal exponential impulse response that is like e^(+alpha*n) for n<0
and then zero after that and, if alpha is positive, it has a pole
outside the unit circle and it's ROC is |z|>1.  dunno what you would
do with the thing, but i s'pose someone has written a paper or two
about it.

r b-j

>i don'r really fiddle with issues regarding ROC and such anymore.  i
>can't really understand how to deal with (simulate or not) an acausal
>IIR filter with exponential components that blow up to infinity.  but
>for an FIR, it's no problem.  if you can set aside a certain finite
>amount of delay, you can deal with any acausal FIR fine.  and then put
>the delay back and it's causal.  no big deal.
>
>
>r b-j
>

Crazy, I wasn't even going to try thinking in terms of an acausal IIR
filter.  I was thinking more in terms of the FIR coefficients converging to
0 as n approaches +-infinity.  Is an acausal IIR filter even a thing?  Like
a useful thing?

On Apr 23, 1:01&#4294967295;pm, "dszabo" <62466@dsprelated> wrote:
>
...
>
> Is causality a requirement?

not necessarily.

>&#4294967295;Wouldn't that only be a requirement if the
> filter were to be used in real time?

yes, pretty much.

just to make sure the t's are dotted and the i's are crossed, when you
run a non-realtime filter (which is equivalent to a simulation) on a
file of data, you can peer ahead to "future" samples and, in that
sense, the filter is not causal.  but remember that file of data was
recorded some time in the past.  so in reality *no* samples come from
the future.  so in reality *no* real filter, whether running realtime
or not, sees future samples and *all* real filters, realtime or not,
are causal.

but we can hypothesize acausal impulse responses and we can simulate
what such an acausal filter would do given a well-defined input.  and
in that context, i am perfectly comfortable with the concept of
acausality in filters and then we can talk about "zero-phase
filters" (not just linear-phase) and the like.


> It seems like the answer would be 'yeah' based on the definition of the
> inverse Z transform, but the word 'arbitrary' would get get some caviats as
> constraints are imposed, such as causality, stability or convergence of the
> impulse response.

i don'r really fiddle with issues regarding ROC and such anymore.  i
can't really understand how to deal with (simulate or not) an acausal
IIR filter with exponential components that blow up to infinity.  but
for an FIR, it's no problem.  if you can set aside a certain finite
amount of delay, you can deal with any acausal FIR fine.  and then put
the delay back and it's causal.  no big deal.


r b-j

>On Apr 23, 9:28=A0am, "westocl" <31050@dsprelated> wrote:
>> From my knowlege of phase/Magnitude response of digital filters,
minimum
>> and maximum are the only filters whose Magnitude response completely
>> specifies its phase response (some kind of log hilbert relationship..
or
>> whatever).
>>
>> Does this infer that given a system that is non minimum and non maximum
>> phase and given an infinite amount of taps, that one could synthesize
any
>> arbitrary frequency response with an error approaching zero?
>
>virtually infinite number of taps?
>
>as long as the filter is causal, sure, why not?
>
>start with the arbitrary frequency response (both magnitude and phase
>is specified for all frequencies up to Nyquist).   but it's gotta be
>causal, so that means that the real and imaginary parts have a Hilbert
>transform relationship.  sample that frequency response with a zillion
>equally-spaced points.  inverse FFT that frequency response and you
>have the impulse response which are also the tap values.
>
>if adding a finite delay to the response is not a problem, you can
>start out with arbitrary magnitude, "arbitrary" phase, inverse FFT and
>you will see a part of your impulse response precede t=3D0, then just
>delay it enough to make it causal.  (but that delay changes the phase
>response, so it isn't truly arbitrary.)
>
>r b-j
>

Is causality a requirement?  Wouldn't that only be a requirement if the
filter were to be used in real time?

It seems like the answer would be 'yeah' based on the definition of the
inverse Z transform, but the word 'arbitrary' would get get some caviats as
constraints are imposed, such as causality, stability or convergence of the
impulse response.

On Apr 23, 9:28&#4294967295;am, "westocl" <31050@dsprelated> wrote:
> From my knowlege of phase/Magnitude response of digital filters, minimum
> and maximum are the only filters whose Magnitude response completely
> specifies its phase response (some kind of log hilbert relationship.. or
> whatever).
>
> Does this infer that given a system that is non minimum and non maximum
> phase and given an infinite amount of taps, that one could synthesize any
> arbitrary frequency response with an error approaching zero?

virtually infinite number of taps?

as long as the filter is causal, sure, why not?

start with the arbitrary frequency response (both magnitude and phase
is specified for all frequencies up to Nyquist).   but it's gotta be
causal, so that means that the real and imaginary parts have a Hilbert
transform relationship.  sample that frequency response with a zillion
equally-spaced points.  inverse FFT that frequency response and you
have the impulse response which are also the tap values.

if adding a finite delay to the response is not a problem, you can
start out with arbitrary magnitude, "arbitrary" phase, inverse FFT and
you will see a part of your impulse response precede t=0, then just
delay it enough to make it causal.  (but that delay changes the phase
response, so it isn't truly arbitrary.)

r b-j

From my knowlege of phase/Magnitude response of digital filters, minimum
and maximum are the only filters whose Magnitude response completely
specifies its phase response (some kind of log hilbert relationship.. or
whatever).

Does this infer that given a system that is non minimum and non maximum
phase and given an infinite amount of taps, that one could synthesize any
arbitrary frequency response with an error approaching zero?