On Thu, 13 Jun 2002, Edson Brusque (listas) wrote:

> Hello All,
>
>
>     some months ago Olin posted the formula that changed DSP world: :)
>         Filt <-- Filt + (New - Filt)*FFrac
>
>     Saddly, my 8 bit implementation have a problem that I can't surpass:
>         filt = filt + ((sig16)new - (sig16)filt) / 2;

The filter can be written like so:

Filt' = Filt + (New - Filt)*FFrac
      = Filt(1-FFrac) + New*FFrac

Often, the FFrac is the ratio of two integers such that:

FFrac = B/(A+B)
1-FFrac = A/(A+B)

The sum of FFrac and (1-FFrac) is  (A+B)/(A+B) or 1.

Using this nomenclature, the filter can be rewritten:

Filt' = (A*Filt  + B*New)/(A+B)

So far nothing new, just a rearrangement of terms.

Now to apply rounding, there are few tricks that you can perform.

Filt' = (A*Filt + B*New + A*New)/(A+B) - A*New/(A+B)

Filt' = New + (Filt-New) * A/(A+B)        ........... (1)

>
>     The value never goes to 255 because of integer roundings:
>         filt = 254 + (255 - 254) / 2;
>         filt = 254 + (1)/2;
>         filt = 254;

In this filter, A=B=1. If you use equation 1:

filt = 255 + (254 - 255) / 2
     = 255 - 1/2
     = 255

Whoopee!

This rounding also works for 0: New=0, Filt=1

Filt' = 0 + (1-0)/2
      = 1/2
      = 0


One way to implement this would be:

    ; W = New

    subwf  Filt,W    ;W = Filt-New
    subwf  Filt,F    ;Swap New and Filtered values

    movwf  temp      ;Save the difference
    rlf    temp,w    ;put sign bit into carry
    rrf    temp,w    ;signed right shift
    btfsc  temp,7    ;If the difference is negative
     addlw 1         ;  then round down
    subwf  Filt,F


This implementation does have a subtle bug. If the difference between the
new and filtered values is greater than 0x7f, then the filter has a
spurious response. To fix this, you need to check the signs of the
difference versus the sign of the filt or new value. It can be done in 4
more instructions.


BTW, an efficient implementation of this class of recursive, one-pole
digital filters can be found:

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

Scott

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