[Elecraft] Question - for Educational Purposes

[David Woolley (E.L)]

Alan Bloom wrote:
>> 2) The IIR filters have slightly steeper skirts, but ring more. The FIR 
>> filters ring less but are not quite as sharp.
> 
> I believe the IIR filters ring more BECAUSE they have steeper skirts. 
> As I explained in a previous message, FIR and IIR filters have similar
> ringing characteristics if the bandwidth and shape factors are the same.

FIR filters cannot ring in the full sense of the word.  What they can do 
is to generate a finite pulse of a particular frequency, but that pulse 
is never longer than the filter length.  Long filter lengths result in a 
delay in the signal, which can become unacceptable in itself, so systems 
are not designed with extremely long filters.

Some basic examples of (non-ringing - or rather ringing at 0Hz) filters 
are the rolling and exponential average.  The rolling average is the 
average of the last n values and is an FIR filter.  The exponential 
average adds x% of the input to (100-x%) of the previous output and is 
an IIR.

(The simple rolling average is special in that you can use an IIR type 
algorithm to compute it, although the result is still only finite 
impulse response.  That formulation of rolling average requires 2 
additions per sample, whereas the FIR style one requires n.)


-- 
David Woolley
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