FM Demod question

Rick Lyons wrote:

>On Wed, 3 Aug 2005 12:19:12 -0400, "Clay S. Turner"
><Physics@Bellsouth.net> wrote:
>
>  (snipped)
>  
>
>>So with mild oversampling, modest filter lengths are all that are needed.
>>
>>IHTH,
>>
>>Clay
>>    
>>
>
>Hi Clay,
>
>   I agree with you completely.
>
>If moderate oversampling is used, Paul might "get away with" 
>using a "central-difference" differentiator defined by:
>
>y1(n) = [x(n) - x(n-2)]/2
>
>which, happily, has a group delay that's an integer 
>number of samples.
>
>I just discovered an interesting digital differentiator 
>that has a wider freq range of "linear magnitude operation" 
>than the central-difference differentiator.
>That new(?) differentiator is defined by:
>
>y2(n) = -x(n)/16 + x(n-2) -x(n-4) + x(n-6_/16).
>  
>
What does "x(n-6_/16" mean? Is it supposed to be:

y2(n) = -x(n)/16 + x(n-2) - x(n-4) + x(n-6)/16

which has a nice symmetric feel to it?

>This "wider-band" y2(n) differentiator has two additional 
>nice properties.
>
>(1) It's non-unity coefficients are powers of two, so binary 
>shifts can be used instead of coefficient multiplication.
>(2) It's group delay is an integer number of samples 
>making it useful for your proposed FM demod scheme.
>
>I'm thinkin' of including that "y2(n) differentiator" as a 
>"DSP Trick" in the 3rd edition of my book.
>  
>
Steve

Rick Lyons wrote:

   ...

> I'm thinkin' of including that "y2(n) differentiator" as a 
> "DSP Trick" in the 3rd edition of my book.

Hi, Rick.

How about sending it Grant Griffin in the mean time?

Jerry
-- 
Engineering is the art of making what you want from things you can get.
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On Mon, 08 Aug 2005 11:02:48 +0800, Steve Underwood <steveu@dis.org>
wrote:

  (snipped)
>>  
>>
>What does "x(n-6_/16" mean? Is it supposed to be:
>
>y2(n) = -x(n)/16 + x(n-2) - x(n-4) + x(n-6)/16
>
>which has a nice symmetric feel to it?

>Steve

Hi Steve,

  Shoot!  I screwed up.
You are correct, it's "x(n-6)/16".

Thanks,
[-Rick-]

On Sun, 07 Aug 2005 23:06:24 -0400, Jerry Avins <jya@ieee.org> wrote:

>Rick Lyons wrote:
>
>   ...
>
>> I'm thinkin' of including that "y2(n) differentiator" as a 
>> "DSP Trick" in the 3rd edition of my book.
>
>Hi, Rick.
>
>How about sending it Grant Griffin in the mean time?
>
>Jerry

Ah yes, I'll look into that.
Thanks.

See Ya',
[-Rick-]