----- Original Message -----
From: Jose S. Samonte Jr. <dyowee@USA.NET>
To: <PICLIST@MITVMA.MIT.EDU>
Sent: Saturday, January 20, 2001 1:21 PM
Subject: Re: [Re: [PIC]: What is IIR filter?]


How is it done, by software, or hardware?

It can be either. It is often done in a DSP (digital signal processor) which
is a special type of high-performance processor designed for this type of
application. It can be done in a PIC, if the signals are of low enough
frequency for the PIC to be able to keep up (typically sub-audio
frequencies).

Here is a very simple IIR in a pseudocode representation:

    filteredoutput = filteredoutput * (1-X) + newinput * X

where 'X' is a value between 0.0 and 1.0.

When 'X' is 1.0 no filtering takes place because the formula becomes:

    filteredoutput = filtredoutput * 0.0 + newinput * 1.0

When 'X' is 0.0 we ignore the input becuase the formula becomes:

    filteredoutput = filteredoutput * 1.0 + newinput * 0.0

Values in between give varying results. For example, when 'X' is 0.5 we
have:

    filteredoutput = filteredoutput * 0.5 + newinput * 0.5

In other words, the output is average of whatever it used to be and the new
input (sample) value.

After a bunch of samples, what we have is a weighted average of samples (in
theory going back infinitely, hence "I"IR):

1/2 of most recent sample
1/4 of sample before that
1/8 of sample before that
1/16 of sample before that
etc.
etc.
etc.

Note that the series 1/2+1/4+1/8+1/16... sums to 1.0, so the average is in
the same 'scale' as the individual samples.

Bob Ammerman
RAm Systems
(contract development of high performance, high function, low-level
software)

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