On Thu, 15 Jun 2000, Andrew Warren wrote:

> Plunkett, Dennis <PICLIST@MITVMA.MIT.EDU> wrote:
>
> > A short time ago there was a thread on filters, and a suggestion
> > for a long term averaging filter was proposed that went along the
> > lines of:-
> >
> > average = (((temp*width)-average)+newsample)/width
>
>     Actually, Dennis, it was probably:
>
>         average = (((average*width)-average)+newsample)/width
>
>     which is usually simplified to:
>
>         average = (average * (width-1) + newsample) / width.

Which is EXACTLY the form discussed just a few weeks ago! E.g.:

avg = (K1*avg + K2*newsample)/(K1+K2)

In this case, K1 = 15, K2 = 1 and their sum is 16.


>
> > 1/ This filter assumes that the processor is a floating point
>
>     No; the equation is EASILY implemented using integer math.  It
>     works like this:
>
>     1.  Since integer division by a power of 2 is trivial, we make
>     "width" equal to a power of 2.
>
>     2.  Since multiplication by a power of 2 is also trivial, we
>     rewrite the equation thusly:
>
>         average = ((newsample-average) + (width*average)) / width
>
>     If we can make width = 256, the code is absurdly simple... But
>     that's a special case.  Here's the code for width = 16, which is
>     more representative of what'll usually be required:
>
>     ; Written by Andrew Warren (fastfwd@ix.netcom.com).
>     ;
>     ;       (NEW - AVE) + 16*AVE
>     ; AVE = --------------------
>     ;               16

<SNIP>

If you wish to generalize this then check out:

http://www.dattalo.com/technical/software/pic/twist.asm

Which weighs in at 22 cycles for a divisor of 16. Pros: the filter coefficients
are arbitrary and the filter is scalable. Cons: The 'Average' is only 8-bits
instead of 12.


Scott

PS. I doubt it's only me, but it's really refreshing to see Andy posting PIC
code again!