[ibis-macro] Re: On impulse and step responses.
- From: "Walter Katz" <wkatz@xxxxxxxxxx>
- To: <DBanas@xxxxxxxxxx>, "'Todd Westerhoff'" <twesterh@xxxxxxxxxx>
- Date: Wed, 26 Jun 2013 13:30:30 -0400 (EDT)
David,
I believe the definition of a Dirac Delta Function is that the area under
it is 1. The area under a continuous curve is the integral of f(t)*dt. For
a discrete representation of this integral becomes the
sum(f(ti)*(ti+1-ti)). Note that sample_rate is 1/(ti+1-ti). Thus the area
under {1, 0, 0, .} is 1/sample_rate while the area under {<sample_rate>,
0, 0, .} is 1.
Walter
From: ibis-macro-bounce@xxxxxxxxxxxxx
[mailto:ibis-macro-bounce@xxxxxxxxxxxxx] On Behalf Of David Banas
Sent: Wednesday, June 26, 2013 1:07 PM
To: Todd Westerhoff
Cc: ibis-macro@xxxxxxxxxxxxx
Subject: [ibis-macro] Re: On impulse and step responses.
Hi Todd,
There are two things being discussed, which is probably adding to the
confusion.
Firstly, I'm challenging Mike's belief that the discrete time equivalent
to the Dirac delta is the sequence, {<sample_rate>, 0, 0, .}. I believe
the discrete time equivalent to the Dirac delta is the sequence, {1, 0, 0,
.}. I think this one has probably been exhausted, unfortunately without
resolution.
Secondly, the current spec. fails to name the units, which are to be
assumed for the values passed into Init(), via the impulse_matrix
parameter. This is the issue, which is less academic, more practical, and
more worthy of the committee's time. Here is the current relevant
language, excerpted from IBIS v5.1:
"impulse_matrix" points to a memory location where the collection of
channel voltage impulse responses, . The algorithmic model is expected to
modify the impulse responses in place by applying a filtering behavior,
for example, an equalization function, if modeled in the AMI_Init
function. .
(Note that my omissions of any original text are indicated by ellipses,
and any emphasis is entirely mine.)
Now, the language "impulse response" is vague in signal processing
parlance, as it can refer to either:
1. The continuous time "impulse response function", or
2. The discrete time "unit pulse response sequence",
both of which are more precise concepts.
In deciding which of the two interpretations, above, to accept, one notes
the use of the language, "voltage" (i.e. - NOT "volts/sec."), as a
qualifying preface to the term, "impulse response." Therefore, one could
defensibly argue that `2' should be assumed, since the continuous time
impulse response function must have units of "Volts/sec.", as has been
pointed out now numerous times in this discussion.
Further confidence in choice '2' is gained, by noting that ours is a
necessarily discrete time application. (It takes place entirely within the
state space of a digital computer, and the interface between the model and
the rest of the system is a discrete sequence of numbers.)
Finally, the language, "in place by applying a filtering behavior,"
suggests that the model should expect to be receiving values with units
most natural to direct digital filter application to the unmodified input,
which would be "Volts".
-db
From: Todd Westerhoff [mailto:twesterh@xxxxxxxxxx]
Sent: Wednesday, June 26, 2013 7:39 AM
To: David Banas
Cc: ibis-macro@xxxxxxxxxxxxx
Subject: On impulse and step responses.
Dave,
Can I ask you to confirm your initial question on this subject? I want to
make sure I understand what we're saying before we get too deep into the
math.
It seems to me that you've called into question the mathematics behind
impulse responses being created for current IBIS-AMI models, and therefore
how IBIS-AMI models must be written to process those impulse responses.
If there is indeed a problem with the math, it follows that the current
standard would need to be either updated or extended, depending on how the
details play out.
Is that what you're saying?
Todd.
Todd Westerhoff
VP, Software Products
Signal Integrity Software Inc. . www.sisoft.com
6 Clock Tower Place . Suite 250 . Maynard, MA 01754
(978) 461-0449 x24 . twesterh@xxxxxxxxxx
"I want to live like that"
-Sidewalk Prophets
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