This is a multi-part message in MIME format.

------=_NextPart_000_0019_01C69C58.D1316C10
Content-Type: text/plain; format=flowed; charset="iso-8859-1";
	reply-type=original
Content-Transfer-Encoding: 7bit

Kevin wrote:
> Yes, what is meant by two poles ?

In this context, a pole means a single simple filter.  In analog, one RC
creates a single pole.  A simple iterative equation for a single pole low
pass filter is

  FILT <-- FILT + FF(NEW - FILT)

where FILT is the filter output value, NEW is the filter input value this
iteration, and FF is an adjustment factor intended to range between 0
(infinitely heavy filter, output never changes) to 1 (no filtering at all,
output follows input).  The nice thing about this equation is that it's easy
to compute, especially when FF is 1 / 2**N where N is an integer.  In other
words, FF could be 1/4, 1/8, 1/16, etc.  In those cases, the multiply by FF
can be performed by a right shift of N bits.

This type of filter is the same as a RC low pass filter in the analog
domain.  Just like you can use several RC filters in series, you can use
several of these digital filters in series.  Each one of the operations
described by this equation is a pole.  This is like connecting the output of
one RC low pass filter to the input of another with a buffer amp in between.
For example, a two pole digital low pass filter based on the above equation
is:

  FILT1 <-- FILT1 + FF1(NEW - FILT1)
  FILT2 <-- FILT2 + FF2(FILT1 - FILT2)

The overall input is NEW and the output FILT2.

>> By shifting 8 bits?
> I understand how to shift 8 bits, but why ?

I was referring to the right shift to realize the multiply by FF.  Using a
shift value of 8 bits means FF = 1/256.

> Normally, I would take 50 10bit adc readings, add them and
> then divied by 50 to get an average result.

That takes a lot of memory and cycles.  At the very least it would be better
to average 32 or 64 readings.  The expensive divide by the number of
readings then becomes just an inexpensive right shift.

This type of filter is called a box filter.  It's not that great in terms of
frequency response, random noise attenuation compared to the filter I
described above.

> What is settling time ?

I was referring to the settling time, or step response time of the filter.
If everything starts out at zero, then you change the input instantaneously
to 1, how fast will the output follow?  Since it is an exponential
approaching 1, it is not meaningful to ask how long it takes to get to 1.
However, you can talk about how long it takes to get various fractions of
the way there.  I use my FILTBITS or PLOTFILT programs to show me the step
response of filters given the FF values for each pole.  Actually the command
line values are in bits of shift rather than FF directly.  I have attached a
step response plot of two poles each with 8 shift bits (FF = 1/256 for each
pole).  From this you can see that this filter settles to about 90% in 1000
iterations.

> Yes How is 93% arrived at and what is it's significance?

>From the plot you can see that the filter reaches about 93% of its final
value at 1100 iterations.

> Why shifting by 8 bits is particularly trivial?
> I assume it has something to do with a bit mask,
> Or is achieved by a single instruction ?

No, it's because the machine addresses memory in 8 bit chunks called bytes.
Therefore there is no need to "shift" a value right 8 bits, you just read it
starting 1 byte into it.

> Why is 2 x 8 bits a lot of random noise attenuations?

Look at what happens when NEW in the top equation has a glitch one
iteration.  FF of that glitch will make it to the output.  For two poles,
FF1*FF2 of the glitch will make it to the output.  If you express the FF
values in terms of the bits shifted, then the glitch is attenuated by 2**N
where N is the sum of all the shift bits for all the poles.  Two poles of 8
shift bits each (FF1 = FF2 = 1/256) attenuates a glitch, or any random
noise, by 16 bits or 1/65536.

------=_NextPart_000_0019_01C69C58.D1316C10
Content-Type: image/gif;
	name="x.gif"
Content-Transfer-Encoding: base64
Content-Disposition: attachment;
	filename="x.gif"
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------=_NextPart_000_0019_01C69C58.D1316C10
Content-Type: text/plain; charset="us-ascii"
MIME-Version: 1.0
Content-Transfer-Encoding: 7bit
Content-Disposition: inline

-- 
http://www.piclist.com PIC/SX FAQ & list archive
View/change your membership options at
http://mailman.mit.edu/mailman/listinfo/piclist

------=_NextPart_000_0019_01C69C58.D1316C10--


******************************************************************
Embed Inc, Littleton Massachusetts, (978) 742-9014.  #1 PIC
consultant in 2004 program year.  http://www.embedinc.com/products