On Sat, 02 Aug 2014 01:48:58 -0500, "SBR123" <100967@dsprelated>
wrote:

>Hello,

Hello mysterious Mr. SBR123,

>I am brushing up on the filter design method using Z-transform, pole/zero
>method. I believe the complexity of the filter is directly proportional to
>the number of poles and zeros I use to design a filter.

That's a broad statement.  Take care in making 
broad (what you think is always true) statements 
about digital filters.  As soon as you make a statement 
that you think is always true, someone will give you 
an example where your statement is NOT true.(This has 
happened to me more than once.)

For example, I can think of a linear-phase tapped-delay 
line FIR that has 100 zeros on the z-plane.  That 
seems like a high-compexity filter, but it's not 
complicated at all.  The block diagram of the (100-zeros) 
FIR filter I have in mind contains only one adder 
and *NO* multipliers.

> Similarly, the
>better (precise) the frequency response, higher is the complexity of the
>filter.
>
>Can the experts weigh in here please.

Well, you have not defined what you mean by the 
word "complexity."  Does that word mean "the order of 
the numerator and denominator polynomials in 
a filter's z-domain transfer function"?   Or perhaps 
your word "complexity" means the number of arithmetic 
operations needed to compute a single filter output 
sample.

The FIR filter I mentioned above has a high-order 
polynomial in its z-domain transfer function, but 
it requires only one addition operation to compute 
a filter output sample.  (Not to be too mysterious 
here, ...that filter is called a "comb filter.")

>Also, more from a theoretical and conceptual perspective, I look at a
>filter more as a system that removes something we don't want. Given this
>understanding, when designing a filter, is it not enough if I just play
>around with zeros to make sure everything that is not needed is
>appropriately supressed?. Why is there a need to use poles?

Well, to have high performance (flat passband response. 
narrow transition regions, high attenuation in the 
stopband) a filter is needed that has a long 
time-domain impulse response (many nonzero-valued samples).  
So how do we build digital filters having long impulse 
responses?  Two ways.  Either (1) a tapped-delay line FIR 
filter having many delay elements, or (2) an IIR filter 
with poles that are located close to the inside of the 
unit circle on the z-plane.

The IIR filter will require fewer arithmetic operations 
per output sample than the FIR filter.  However, the FIR 
filter can have linear phase which the IIR filter 
can never have.  Pick your poison SBR123.

Good Luck,
[-Rick-]

On Saturday, August 2, 2014 2:48:58 AM UTC-4, SBR123 wrote:
> Hello,
> 
> 
> 
> I am brushing up on the filter design method using Z-transform, pole/zero
> 
> method. I believe the complexity of the filter is directly proportional to
> 
> the number of poles and zeros I use to design a filter. Similarly, the
> 
> better (precise) the frequency response, higher is the complexity of the
> 
> filter.
> 
> 
> 
> Can the experts weigh in here please.
> 
> 
> 
> Also, more from a theoretical and conceptual perspective, I look at a
> 
> filter more as a system that removes something we don't want. Given this
> 
> understanding, when designing a filter, is it not enough if I just play
> 
> around with zeros to make sure everything that is not needed is
> 
> appropriately supressed?. Why is there a need to use poles?
> 
> 
> 
> Thank you 	 
> 
> 
> 
> _____________________________		
> 
> Posted through www.DSPRelated.com

SBR123,

"Why is there a need to use poles?"

Look in your text about why someone would use IIR filters rather than FIR filters.

Dirk

On Saturday, August 2, 2014 6:48:58 PM UTC+12, SBR123 wrote:
> Hello,
> 
> 
> 
> I am brushing up on the filter design method using Z-transform, pole/zero
> 
> method. I believe the complexity of the filter is directly proportional to
> 
> the number of poles and zeros I use to design a filter. Similarly, the
> 
> better (precise) the frequency response, higher is the complexity of the
> 
> filter.
> 
> 
> 
> Can the experts weigh in here please.
> 
> 
> 
> Also, more from a theoretical and conceptual perspective, I look at a
> 
> filter more as a system that removes something we don't want. Given this
> 
> understanding, when designing a filter, is it not enough if I just play
> 
> around with zeros to make sure everything that is not needed is
> 
> appropriately supressed?. Why is there a need to use poles?

If you require a lower-order filter then poles are the way. You need more zeros to approximate the effect of poles (for digital filters that is - for analogue we usually have poles and/or zeros) You can also get linear phase with FIR filters and this is far harder with poles.

Hello,

I am brushing up on the filter design method using Z-transform, pole/zero
method. I believe the complexity of the filter is directly proportional to
the number of poles and zeros I use to design a filter. Similarly, the
better (precise) the frequency response, higher is the complexity of the
filter.

Can the experts weigh in here please.

Also, more from a theoretical and conceptual perspective, I look at a
filter more as a system that removes something we don't want. Given this
understanding, when designing a filter, is it not enough if I just play
around with zeros to make sure everything that is not needed is
appropriately supressed?. Why is there a need to use poles?

Thank you 	 

_____________________________		
Posted through www.DSPRelated.com