Parallel form filter design

Hi!

I have a transfer function coefficients as following:

[b,a] = ellip(4,.2,40,[.41 .47]);

I'd like to factor this system into its PFE using

[r,p,k] = residue(b,a)

Then, I'd like to implement a filter which uses a parallel combination of second-order subsections. To do this, I need to combine each complex pole with its complex conjugate so that the overall second order subsections will have real valued coefficients. Hence; I selected four pairs of first order terms and recombined them into second order subsections using "residue" function. How can I store the coefficients of the resulting second-order subsections in the matrices c and d so that each row corresponds to one second order system?

I tried to do this but I don't know whether it's correct or not?

Can anybody please give me an idea? Any help would be appreciated.

Answer 1

[Star Strider]

I am not quite certain what you want to do.

To express your elliptic filter as second-order-sections, the Signal Processing Toolbox has a built-in function to do just that.

I would just do:

[z,p,k] = ellip(4,0.2,40,[.41 .47]);
[sos,g] = zp2sos(z,p,k);

figure
freqz(sos, 2^14)

The freqz plot is the Bode plot of the filter.

Note that th filtfilt function can use the ‘sos’ and ‘g’ outputs to define your filter to filter your signal.