# Pole-Zero Plots Diagram Explanation

I experiment with the coefficient quantization in an IIR filter. I change some values like the passband ripple and also how many bits i want for the quantization method. In the first picture i have 1db passband ripple , 'round'and 7-bits as the quantization method: In the second picture i have 1.3db as the passband ripple ,'round' and 6-bits as quantization method. These are the PZP diagrams. I dont understand how i can extract useful information from the diagrams in order to say which design is better or to make comparisons between these 2 designs.How the Poles and Zeros affect my decision for what is better?

edit: the images becomes bigger and more visible when you copy the url and open or select view image. Also with the green is the quantized and with blue the un-quantized coefficients.

edit2:As Matt asks for magnitude frequency response I have add the extra information:

1db passband ripple , 'round'and 7-bits   1.3db as the passband ripple ,'round' and 6-bits   I want to find a set of quantized coefficients that meet the specification with the minimum number of bits. My specification is an 8th-order IIR filter with the following transfer function magnitude response: \begin{align*} 0\,\mathrm{db} \pm 1.5 \,\mathrm{db} & \quad \text{for } \quad 0.2<|v|<0.3 \cr \lt −60\,\mathrm{db} & \quad\text{for } \quad |v|<0.14\text{ and } |v|>0.36 \end{align*}

I use this matlab function: $[b,a]=ellip(n,Rp,Rs,Wp) ,$

after some trials i found that (the filter is implemented using second-order sections) : $[b,a]=ellip(4,1,60,2*[0.2,0.3])$ and using 7-bit quantization i take the diagram above that i think verify the specification (if i make a mistake please correct me) ,

but if a use: $[b,a]=ellip(4,1.3,60,2*[0.2,0.3])$ and 6-bit quantization also i take a reasonable result. My concern is if my thought and procedure is correct or i have a mistake and i need to stick with 7-bits quantization?

• As far as I can see, the filters you designed satisfy your specs. One thing I noticed is the following: in your spec it says $\pm 1.5$dB passband ripple. Note that the passband ripple $R_p$ for the ellip() function is defined as a variation in the range $[0,-R_p]$ dB. That means that your allowed value for $R_p$ is actually 3 dB and not 1.5 dB. Of course you need some margin to take coefficient quantization into account. Furthermore, after you have a design, you must scale your filter such that the magnitude response oscillates between +1.5 dB and -1.5 dB in the passband ... Apr 14, 2013 at 15:55
• ... according to you spec. The filters obtained by ellip() always have their maximum at 0dB and go down to $-R_p$ at the passband edge. Apr 14, 2013 at 15:57
It is indeed hard to compare the two designs just using the pole-zero diagrams. I think it would be much more useful to have a look at the (magnitude of the) frequency responses, and compare the change of the frequency response before and after coefficient quantization. The only thing I can say from looking at the pole-zero plots is that you have designed an eighth order bandpass filter with center frequency $f_s/4$ (by $f_s$ I mean the sampling frequency).