An IIR filter gain questio

Rick Lyons wrote:
>
> Well, ... sorry to hear about those physical problems.

i'm just being a wus.

> I guess I don't feel so bad now
> knowing I'm not the only one who's fallin'
> apart.  I can't see street signs while I'm
> driving at night, I haven't stopped by
> my ex-wife's place to provide any "special service"
> for many months,

hmmmm.  interesting "ex-"relationship.

> & I'm doomed forever to take
> four metformin tablets every stinkin' day.

had to look that one up.  is it in lieu of sticking yourself 4 times a
day?

man, when you look up the price of these things, them druggie companies
do about as well as the oil companies.  makes me mad as hell (and smug)
that they stole the election 5 1/2 years ago.

> Actress Betty Davis said it many years ago,
> "Old age ain't for sissies."
> Good Hell, she was NOT jokin'.

yeah.  and i don't even know the half of it yet.

r b-j

On 13 May 2006 22:47:55 -0700, "robert bristow-johnson"
<rbj@audioimagination.com> wrote:

>Rick Lyons wrote:
>
>>
>> Reviewing the exciting narrative on "IIR filter
>> scaling" in Dale Grover's and John Deller' DSP
>> book, I have arrived at the IIR filter shown as:
>>
>>  x --->(+)--1/Gb-->------Gf*b0--->(+)---> y
>>         ^           |              ^
>>         |         [z^-1]           |
>>         |           |              |
>>        (+)<--a1/Gb--+----Gf*b1--->(+)
>>         ^           |              ^
>>         |         [z^-1]           |
>>         |           |              |
>>         +---a2/Gb---+----Gf*b2-----+
>>
>> That is, the original IIR filter's feedback coeffs
>> are divided by a feedback gain factor "Gb",
>> and feedforward coeffs are multiplied by a
>> feedforward gain factor "Gf".  The result of
>> using these two Gb & Gf gain factors is a new biquad
>> whose gain is the original biquad's gain multiplied
>> by "Gb times Gf" (GbGf).


Hi R B-J,

>i think the feedforward gain of 1/Gb needs to be changed to just "Gb"
>as so:
>
>  x --->(+)---Gb--->------Gf*b0--->(+)---> y
>         ^           |              ^
>         |         [z^-1]           |
>         |           |              |
>        (+)<--a1/Gb--+----Gf*b1--->(+)
>         ^           |              ^
>         |         [z^-1]           |
>         |           |              |
>         +---a2/Gb---+----Gf*b2-----+
>
         ^^^^^^^^^^^^^^^^^^^^^^^^
         ||||||||||||||||||||||||

          R B-J's Figure 1

Yes, yes.  My MATLAB modeling is correct, but 
my original block diagram was drawn incorrectly.
Your "R B-J's Figure 1" above is correct.
Thanks for catchin that "boo boo" in my 
drawing.


>which becomes:
>
> x -Gb->(+)-------->------Gf*b0--->(+)---> y
>         ^           |              ^
>         Gb        [z^-1]           |
>         |           |              |
>        (+)<--a1/Gb--+----Gf*b1--->(+)
>         ^           |              ^
>         |         [z^-1]           |
>         |           |              |
>         +---a2/Gb---+----Gf*b2-----+

         ^^^^^^^^^^^^^^^^^^^^^^^^
         ||||||||||||||||||||||||

          R B-J's Figure 2
>
>
>and thus:
>
> x -Gb->(+)-------->------Gf*b0--->(+)---> y
>         ^           |              ^
>         |         [z^-1]           |
>         |           |              |
>        (+)<---a1----+----Gf*b1--->(+)
>         ^           |              ^
>         |         [z^-1]           |
>         |           |              |
>         +-----a2----+----Gf*b2-----+

         ^^^^^^^^^^^^^^^^^^^^^^^^
         ||||||||||||||||||||||||

          R B-J's Figure 3
>

Ah ha.  Now this an aspect I didn't see before.
I wanted to avoid having a gain factor before the 
1st adder, in the block diagram, because having a 
gain factor there that's less than unity degrades 
the input signal-to-noise (SNR).  But you've now 
made me realize that having Gb less than unity in 
your "R B-J's Figure 1" is gonna reduce the SNR of 
the input to my IIR filter whether I like it or not.
Sheece... Thanks for pointing that out to me Robert.

   (snipped)
>
>i presume the Gf thingie is a non-issue.  that sorta thing is done all
>the time with IIRs.  with Gb, you are simply scaling those states with
>Gb.  if you're doing that for fixed-point issues, i think there are
>better ways to either think about it or to implement it (like ditch the
>DF2 and do it with DF1).  for floating-point, it seems pointless to me,
>but there is lotsa esoteric stuff that i dunno. 
>
>r b-j

Some time ago I posted a wise-crack here on comp.dsp 
that, "IIR filters are for sissies."  
OK OK, I take it back.

Thanks Robert, ... or as we're being forced to 
say in California, "Thanks Roberto."

[-Rick-]
(Also,... "Thanks" to Greg Berchin for adding 
his comments to this thread.)