[ibis-macro] Re: On impulse and step responses.
- From: "Dmitriev-Zdorov, Vladimir" <vladimir_dmitriev-zdorov@xxxxxxxxxx>
- To: "DBanas@xxxxxxxxxx" <DBanas@xxxxxxxxxx>, "fangyi_rao@xxxxxxxxxxx" <fangyi_rao@xxxxxxxxxxx>, "ibis-macro@xxxxxxxxxxxxx" <ibis-macro@xxxxxxxxxxxxx>
- Date: Tue, 25 Jun 2013 16:46:13 +0000
Hi David,
Maybe you'll like the following interpretation more:
- Step response shows the "voltage" (but in other applications could be
current, wave etc.) when the system transitions from its initial zero state
into another state forced by applying the step-wise input stimulus.
- Impulse response characterizes a speed with which such transition
happens. As speed, it has 1/sec factor in its dimension, and peaks where the
step transition changes most quickly. Before time zero, and after transition
settles, its speed is zero. That's why impulse response is assumed to be zero
for time<0, and end there, too. As you see, it has a clear physical meaning.
The speed of changing the output voltage is tremendous. It's not uncommon that
you get 1V change in 0.1ns, that's why you get the values of 1e10 Volt/sec and
more.
Vladimir
From: ibis-macro-bounce@xxxxxxxxxxxxx [mailto:ibis-macro-bounce@xxxxxxxxxxxxx]
On Behalf Of David Banas
Sent: Tuesday, June 25, 2013 10:04 AM
To: fangyi_rao@xxxxxxxxxxx; ibis-macro@xxxxxxxxxxxxx
Subject: [ibis-macro] Re: On impulse and step responses.
Hi Fangyi,
Thanks for the reply.
Please, see below.
Thanks,
-db
From: fangyi_rao@xxxxxxxxxxx [mailto:fangyi_rao@xxxxxxxxxxx]
Sent: Thursday, June 20, 2013 8:18 AM
To: David Banas; ibis-macro@xxxxxxxxxxxxx
Subject: RE: On impulse and step responses.
David;
Step response has an unit of volt. Impulse response, which is the derivative of
step response by definition, has an unit of volt/sec.
[David Banas] If this discussion pertained to the continuous time domain, I
would agree with you, but it doesn't. This discussion pertains to the discrete
time domain. (It has to, since we're sending in a discrete set of samples,
taken at a uniform sampling interval, to Init().) And, in that domain, both
quantities must have the same unit, since we require:
[cid:image003.png@01CE7191.3566CFD0]
where {uk} is the "unit step response sequence" and {hi} the "unit pulse
response sequence" of the LSI discrete time system being discussed, and I have
taken the liberty of assuming we're only interested in describing causal
systems. In our particular application, the most reasonable unit for these two
sequences seems to be "Volt", which is why I'm very perplexed as to why several
of us seem to feel that "Volts/sec." is the proper unit to be sending into
Init(). Does our current spec. call out the exact units to be used?
Also, please keep in mind that the Dirac delta function has an unit of 1/sec.
Regards,
Fangyi
From: ibis-macro-bounce@xxxxxxxxxxxxx<mailto:ibis-macro-bounce@xxxxxxxxxxxxx>
[mailto:ibis-macro-bounce@xxxxxxxxxxxxx] On Behalf Of David Banas
Sent: Thursday, June 20, 2013 7:50 AM
To: ibis-macro@xxxxxxxxxxxxx<mailto:ibis-macro@xxxxxxxxxxxxx>
Subject: [ibis-macro] On impulse and step responses.
Hi all,
In our work, we often take as a priori that the impulse response is the time
derivative of the step response. As I puzzle over this further, I realize that
I'm stumped by something very fundamental, which is this:
A quantity, which is the time derivative of some other quantity, cannot have
the same units as that other quantity. And, yet, when we
discuss/measure/simulate either a step response or an impulse response, we
expect to be talking about / measuring / viewing a voltage as a function of
time, in both cases! How can this be?
Thanks,
-db
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