On 2008-07-07, Jim Lesurf wrote:
In article , John Phillips
wrote:
For example, if you take a perfect square wave with all of its
harmonics, and mathematically remove all of those above a certain point
you will see a waveform with ringing. I think this is referred to as
Gibbs' Phenomenon.

The distinction I think people have latched onto is that if you use one of
the familiar types of analogue LP filter, then any ringing tends to occur
after the transitions of the square-wave. This tends to be interpreted as a
'causal' requirement. That the filter can't react to the transition until
it occurs. Although this interpretation is rather shakey since it is quite
possible for the entire pattern to have been delayed in transit though the
filter, so any 'pre' transition ringing may be entirely causal - even with
an analogue system.

This is one of the issues I see. Nothing is, in practice, acausal.

The fact that in the square wave Gibbs Phenomenon example something
appears to happen before the transition is nothing at all to do
with acausality. There are differences in time-domain behaviour
between difital and analogue filters but I ask myself whether applying
"conventional wisdom" learned from the analogue case to the digital case
is rather flawed.

... snip ...
I note though that Meridian have now used a filter that gets all the
ringing post transitions. Suspect this was based on Peter Craven's work.
The downside it a tendency to phase spread, I assume.

Yes. I saw that from Meridian and asked myself if it was marketing
or engineering.

... snip ...
See also the articles on this on audiomisc in the 'hearing' section which
also considers hearing nonlinearity in this context.

OK I will look.

FWIW I am less than convinced ringing is audible in time symmetric filters.
It seems to be another of the popular ideas in audio for which I've not
personally found any reliable evidence. But given hearing nonlinearities,
it might be audible. So I would not totally dismiss the idea from what I
know at present.

Agreed.

--
John Phillips