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From: Randy Yates on 18 Jun 2010 11:21
Is there a simple expression for the group delay of a CIC filter stage
in terms of the differential delay (M) and the rate change R?
--
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Digital Signal Labs % Who are you and who am I?"
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From: Rick Lyons on 20 Jun 2010 16:46
On Fri, 18 Jun 2010 11:21:37 -0400, Randy Yates <yates(a)ieee.org>
wrote:

>Is there a simple expression for the group delay of a CIC filter stage
>in terms of the differential delay (M) and the rate change R?

Hi Randy,
I know you have the 2nd edition of my DSP book.
Looking at Figure 10-17(a), because a CIC decimation filter
(prior to the downsampling process) is merely a
D-point moving averager, the linear-phase CIC filter's
constant group delay is (D-1)/2 samples. Measured in
seconds, the group delay is T*(D-1)/2, where "T" is the
time between samples (measured in seconds).

Randy, I show this same result, with a bit of mathematics,
on page 233 (near Equation (5-40)) of the hardcopy material
for my 3rd edition that you reviewed for Prentice Hall.

I'll bet you already knew the above.

Now if you're asking what's the group delay of, for example
a decimating CIC filter, *after* the downsampling by "R"
process, darn, I haven't thought about that before.

As the guys here say, shooting from the hip, my first
thought is that the group delay (measured in seconds)
of a decimating CIC filter followed by downsampling by "R"
is also T*(D-1)/2, where "T" is the time between *input*
samples (measured in seconds).

I'll have to think this through carefully and do some
MATLAB modeling, but if I'm wrong someone here will
straighten me out.

See Ya,
[-Rick-]
From: Randy Yates on 20 Jun 2010 21:30
Rick Lyons <R.Lyons@_BOGUS_ieee.org> writes:

> On Fri, 18 Jun 2010 11:21:37 -0400, Randy Yates <yates(a)ieee.org>
> wrote:
>
>>Is there a simple expression for the group delay of a CIC filter stage
>>in terms of the differential delay (M) and the rate change R?
>
> Hi Randy,
> I know you have the 2nd edition of my DSP book.
> Looking at Figure 10-17(a), because a CIC decimation filter
> (prior to the downsampling process) is merely a
> D-point moving averager, the linear-phase CIC filter's
> constant group delay is (D-1)/2 samples. Measured in
> seconds, the group delay is T*(D-1)/2, where "T" is the
> time between samples (measured in seconds).
>
> Randy, I show this same result, with a bit of mathematics,
> on page 233 (near Equation (5-40)) of the hardcopy material
> for my 3rd edition that you reviewed for Prentice Hall.
>
> I'll bet you already knew the above.
>
> Now if you're asking what's the group delay of, for example
> a decimating CIC filter, *after* the downsampling by "R"
> process, darn, I haven't thought about that before.
>
> As the guys here say, shooting from the hip, my first
> thought is that the group delay (measured in seconds)
> of a decimating CIC filter followed by downsampling by "R"
> is also T*(D-1)/2, where "T" is the time between *input*
> samples (measured in seconds).
>
> I'll have to think this through carefully and do some
> MATLAB modeling, but if I'm wrong someone here will
> straighten me out.
>
> See Ya,
> [-Rick-]

Thanks for the response Rick. Unfortunately I hadn't read this
before spending an hour of your time this afternoon on the phone
discussing it! The (embarrassingly) simple answer is (D-1)/2.
--
Randy Yates % "She tells me that she likes me very much,
Digital Signal Labs % but when I try to touch, she makes it
mailto://yates(a)ieee.org % all too clear."
http://www.digitalsignallabs.com % 'Yours Truly, 2095', *Time*, ELO
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