How to combine filter coefficients for multiple stop band filters - Matlab -

i combine several stop band filters single filter understand how filter changes phase when there mutiple bands removed.

this question provides solution 2 filters, if there more 2 filter bands?

here image showing gains , phase of each separate filter.

so questions are:

1. what happens phase if filter data in 5 separate operations
2. can combine filtering steps single step?

i using butter , freqz functions in matlab.

[b,a] = butter(order,cutoff/(fs/2),'high'); [h,w] = freqz(b,a,fs); 

thanks.

the phases , magntudes (db) sum. if want see on matlab need cascate filter, exemple:

% computes coefficients [b1,a1]=butter(8,0.6);           [b2,a2]=butter(8,0.4,'high');    [b3,a3]=butter(8,0.2,'high');    % creates filters h1=dfilt.df2t(b1,a1); h2=dfilt.df2t(b2,a2); h3=dfilt.df2t(b3,a3); % creates cascate filter hcas=dfilt.cascade(h1,h2,h3)    % plot     hcas.freqz()