# filter clarity needed - does no. of coefficients = order = no. of poles and zeros?

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Tom il 21 Mag 2012
does the no. of filter coefficients also equal the order and also the no. of poles and zeros?
thanks
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Matt Fig il 2 Nov 2012
Tom's question
does the no. of filter coefficients also equal the order and also the no. of poles and zeros?
thanks

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### Risposta accettata

Wayne King il 21 Mag 2012
No, not the number of coefficients, but there is a relationship with the order. The order is one less than the number of coefficients. Remember there is a 0-th order coefficient.
For the rational systems that you are dealing with, the number of poles and zeros will be the same and that will be equal to the largest order (numerator or denominator).
If you use butter(), ellip(), then MATLAB will return identical orders for both the numerator and denominator.
[b,a] = butter(10,0.2);
isequal(length(b),length(a))
There will be 10 poles and 10 zeros.
But note that even if the numerator and denominator orders are different.
B = 1;
A = [1 -0.5 0.2];
zplane(B,A)
The number of zeros and poles are identical and that number is equal to the highest order of the numerator or denominator. In the above that is 2.
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Tom il 21 Mag 2012
Thanks loads Wayne - I think I'm getting it now.
From a block diagram I can work out the order (no. of previous input or output values required for the filter to work), the no. of coefficients is one more than this because of the 0th order, i can work out the difference equation, then the Z-transform function, and if I put that into a form that has only positive power values then the roots of the numerator give the zeros (where the filter response is zero) and the roots of the denominator give the poles (where the filter response is maximal).
Does this all sound right?

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