Re: FIR and IIR systems

On 6 Feb., 13:59, Rune Allnor <all...@xxxxxxxxxxxx> wrote:
On 6 Feb, 13:43, Andor <andor.bari...@xxxxxxxxx> wrote:

Markus wrote:
Take my example of the continuous-time FIR. It has no poles, only
zeros, and decays to zero for large frequencies.

Yes, reading the question again word by word you are correct. Your example
is a finite-impulse-response example in continuous-time. Its frequency
response is naturally infinitely wide, but nobody asked for a "physical"
example.

This prompts the following question: which system is more "physical",
the one that has an infinite impulse response or the one that has a
frequency response that extends to infinity ... ?

Do you suggest these types of systems can not be realized?

On the contrary. I'm trying to counter Markus' idea that an infinitely
wide frequency response is somehow "unphysical".

There are a few constraints that 'physical' systems need to obey.
Causality and stability have already been mentioned -- I would add
continuity as well.

I wouldn't. Currently, I'm working on heat transport in multi-layer
systems. This is, for small temperature changes, well described by
linear systems. However, the systems have odd (to us ee's) transfer
functions. For example, the transfer function that relates surface
heat flux (input signal) to surface temperature (output signal) on a
half-infinite solid is

H(w) = 1/sqrt(i w),

and the impulse response is

h(t) = 1/sqrt(pi t), t > 0.
= 0, t <= 0.

Although the system is very physical, it is not continuous at t=0.

And there are the energy and power conservation
laws. I can't see that a spectrum with infinite extent contradicts
any of these? In fact, I remember having seen a theorem that
'physical' systems are required to be of infinite bandwidth or
the time responses are both noncausal and of infinite extent...

I'm not quite sure about that. For some time now, I've been wondering
what is the impulse response of the ideal minimum-phase brickwall
filter (the linear-phase impulse response is the sinc). Such a minimum-
phase filter would have finite bandwidth and have causal impulse
response.

Regards,
Andor


Don't remember the name of the theorem, though, but this
*might* have been a corollary to the Wiener-Kintchine theorem.

Yeah, I like hot dogs too :-).
.

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