[ibis-macro] Re: On impulse and step responses.
- From: Kumar Keshavan <ckumar@xxxxxxxxxxx>
- To: "fangyi_rao@xxxxxxxxxxx" <fangyi_rao@xxxxxxxxxxx>, "DBanas@xxxxxxxxxx" <DBanas@xxxxxxxxxx>, "ibis-macro@xxxxxxxxxxxxx" <ibis-macro@xxxxxxxxxxxxx>
- Date: Tue, 25 Jun 2013 17:40:40 -0700
on another note whike the sample interval implies uniform uniform time step,
iIt does not necessarily result in discrete samples in a bit interval. For
example you can have a sampling interval of 3ps. Such timesteps may be
necessary to make apple to apple comparison with time domain simulations
________________________________________
From: ibis-macro-bounce@xxxxxxxxxxxxx [ibis-macro-bounce@xxxxxxxxxxxxx] On
Behalf Of fangyi_rao@xxxxxxxxxxx [fangyi_rao@xxxxxxxxxxx]
Sent: Tuesday, June 25, 2013 6:39 PM
To: DBanas@xxxxxxxxxx; ibis-macro@xxxxxxxxxxxxx
Subject: [ibis-macro] Re: On impulse and step responses.
Hi, David;
You brought up a good point and let me try to explain it. Impulse response, by
its mathematical definition, is a continuous function. A physical channel’s
impulse response, unlike digital filters, is continuous in time by nature. By
definition, output and input signals are related by impulse response as
[cid:image004.png@01CE71BA.2BDA0FD0]
For this relation to hold, h(t) must have 1/sec in its unit.
The physical world is continuous in time. Now, let’s see how discrete time
comes into the picture. We need discrete time because we need to evaluate this
integral numerically. The simplest way is the zero-th order discretization, as
you pointed out.
[cid:image005.png@01CE71BA.2BDA0FD0]
It looks like a FIR with taps h(n•t)*•t (here I used uniform discrete time step
but you can of course use non-uniform steps). However, the tap coefficients
equal h(n•t)*•t ONLY if you are doing zero-th order discretization. If you
employ higher order discretization such as trapezoidal to evaluate the
integral, the tap coefficients no longer equal to h(n•t)*•t and depend on the
order.
Note that EDA tools can employ any discretization scheme when evaluating the
integral. To allow that freedom, it’s best to stay with the original continuous
time definition and unit for impulse response. If we interpret the impulse as a
FIR, we‘ll have to specify in what discretization sense.
Just for the sake of argument, an EDA tool can also potentially evaluate the
integral w/o any discretization. It can do a pole/zero fit on h(t) and perform
analytic integral with x(t). Another reason not to define h(t) as a FIR.
Regards,
Fangyi
From: David Banas [mailto:DBanas@xxxxxxxxxx]
Sent: Tuesday, June 25, 2013 9:04 AM
To: RAO,FANGYI (A-USA,ex1); ibis-macro@xxxxxxxxxxxxx
Subject: 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>
[mailto:fangyi_rao@xxxxxxxxxxx]
Sent: Thursday, June 20, 2013 8:18 AM
To: David Banas; ibis-macro@xxxxxxxxxxxxx<mailto: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:image007.png@01CE71BA.2BDA0FD0]
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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