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Hello friends.
I have an apparently unsolvable problem:
I have a given IIR filter (they give me the poles and the zeros).
The filter was originally sampled at a given (very high) frequency.
I also have a signal, which is sampled at a much lower rate.
When I filter my signal, I have to resample it at the same (high and 
unuseful) frequency of the filter, in order to have a correct 
filtering.
I'd like instead to filter my signal at its original (low) rate.
Is it possible to lower the frequency of an IIR (just repositioning 
the zeros and the poles)? If that's possible, I could filter my 
signal at the original rate, saving much computational time!
Please, let me know if there's any solution ;-)
Bye
Stefano
	

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Interesting problem stefan!!!!!!! 
when ever a signal or system is down sampled ie its sampling rate is lowrered from its high
value, then in its Z-Transform function the Z is replaced by Z raised to the power of inverse
of M. That shows that poles and zeroes are changed by (increased or decreased I haven't worked
out) M times and the positioning I feel remains the same. 
Take a 10th order IIR  filter and replace Z with Z raised to the power of inverse of M and see
how many poles and zeroes u are now getting and also u can see that the position of Poles and
Zeroes remain the same. 
This is just a response which came spontaneously after looking at ur query. I haven't seriously
worket it out. Hope my answer could help atleast partially to u. 
with Regards 
Madhusudhan 

 stefanosorrentino <shepan@shep...> wrote:Hello friends.
I have an apparently unsolvable problem:
I have a given IIR filter (they give me the poles and the zeros).
The filter was originally sampled at a given (very high) frequency.
I also have a signal, which is sampled at a much lower rate.
When I filter my signal, I have to resample it at the same (high and 
unuseful) frequency of the filter, in order to have a correct 
filtering.
I'd like instead to filter my signal at its original (low) rate.
Is it possible to lower the frequency of an IIR (just repositioning 
the zeros and the poles)? If that's possible, I could filter my 
signal at the original rate, saving much computational time!
Please, let me know if there's any solution ;-)
Bye
Stefano
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Since Z is replaced by Z raised to the power of inverse of M ( where M is the decimation
factor ), so all the poles and zeroes not only radially move but also their position with
respect to the real axis also changes (angular displacement). But it ensures stable filter but
since poles move towards unit circle there is a possibility of the system to have tendency to
go into oscillations. 
in my earlier mail I wrote that the no of Poles and Zeroes may get altered. 
with best regards
Madhusudhan
 stefanosorrentino <shepan@shep...> wrote:Hello friends.
I have an apparently unsolvable problem:
I have a given IIR filter (they give me the poles and the zeros).
The filter was originally sampled at a given (very high) frequency.
I also have a signal, which is sampled at a much lower rate.
When I filter my signal, I have to resample it at the same (high and 
unuseful) frequency of the filter, in order to have a correct 
filtering.
I'd like instead to filter my signal at its original (low) rate.
Is it possible to lower the frequency of an IIR (just repositioning 
the zeros and the poles)? If that's possible, I could filter my 
signal at the original rate, saving much computational time!
Please, let me know if there's any solution ;-)
Bye
Stefano
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