On 05/02/2013 01:26 AM, Richard Dobson wrote:
On 01/05/2013 23:52, Sampo Syreeni wrote:
...
Still, do give me your definition of time-invariant. Perhaps there are
stronger definitions I haven't heard of yet, and which can be useful in
e.g. more fine grained analysis.
I have always understood it to mean that the behaviour is not dependent
upon ~when~ the signal is injected. Thus, a plain delay is TI because
everything is always delayed the same way; while a modulated effect such
as a flanger (maybe using a variable delay) is not TI as exactly what
comes out depends in the time something goes in.
i guess that's pretty much sampo's definition.
but according to him, a compressor is time-invariant because it only
depends on previous states of the input signal, so the result will be
the same regardless of when you begin injecting the signal.
iiuc, fons would consider this a time-variant system, because its
behaviour at any single point in time is not constant (it depends on
previous input according to RMS circuit, previous gain reduction and
attack/release times).
so i guess the conceptual difference is whether the system's behaviour
depends only on the input signal, or on some external factor, like
modulation.
for practical purposes, i guess fons' definition is more useful, because
then the term "LTI" system is strictly limited to something that can be
fully described with an impulse response.
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