Two Dimensional Filter Design From One Dimensional Prototype Filter Rotation

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MFK 2021-11-17

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https://ww2.mathworks.cn/matlabcentral/answers/1588979-two-dimensional-filter-design-from-one-dimensional-prototype-filter-rotation

编辑： MFK 2021-11-17

I designed an one dimensional filter and it's coefficients (c_estimated) are below.

c_estimated=[-0.0122879538101070,-0.00936229970020011,-0.00533047175279384,-0.000879240291169325,0.00442937840660125,0.0100103547115524,0.0154584938349991,0.0167766116340094,0.0191819943698554,0.0176610078539290,0.0134142321969706,0.00738896103686041,4.78621117449734e-06,-0.00772157595624712,-0.0154347847351846,-0.0197808870552875,-0.0263928918670513,-0.0273375787436225,-0.0233470415500297,-0.0170161782790395,-0.00754797342458864,0.00285659633541593,0.0147348228320903,0.0242369753090141,0.0368617303382725,0.0434986249766230,0.0434671612024621,0.0382913985317041,0.0288908273136430,0.0150280740481253,-0.00283379591508635,-0.0227413540011186,-0.0483224283910802,-0.0701072149732580,-0.0884040352627693,-0.103554572311423,-0.113759407155347,-0.118674284825946,-0.117305705133992,-0.112030561859145,-0.0985998030610725,-0.0848482759616751,-0.0690582961602349,-0.0516352181816368,-0.0351498851798397,-0.0204613014255703,-0.0100583312660474,-0.000275550678307800,0.00339070217939305];
[h,w]=freqz(c_estimated,1,1024);
w=w/pi;
h=abs(h);
figure,plot(w,h);
title('Frequency Response of Prototype Filter');
figure,plot(w,mag2db(h));
title('Frequency Response in dB of Prototype Filter');

After that I modulated this filter coeffients with below code and create a 4 channel filter bank;

wp=0.1250;  %pass band normalized frequency
M=4;        %filter bank channel number
N=49;       %coefficient size
x_coeff(1,:)=c_estimated.*exp(j*2*(wp/2)*pi*(1:N));
    x1_coeff(1,:)=x_coeff;
    [hxx(:,1),wxx(:,1)]=freqz(x_coeff,1,1024);
    for i=1:M-1
        x1_coeff(i+1,:)=x_coeff.*exp(j*2*wp*i*pi*(1:N));
        [hxx(:,i+1),wxx(:,i+1)]=freqz(x1_coeff(i+1,:),1,1024);
    end
wxx=wxx/pi;
hxx=abs(hxx);
figure,plot(wxx,hxx);
title('Frequency Response')
figure,plot(wxx,mag2db(hxx));
title('Frequency Response in dB')   

Now I want to rotate this filter channels seperately around vertical axis and get a 2 dimensional circularly symmetric filter frequency responses. As a result I want to get circularly symmetric low pass from channel 1, circularly symmetric band pass filters from channel 2 and 3, circularly symmetric high pass filter from channel 4. But I'm stuck and do not know what to do. What am I supposed to do? Thanks for all your help.

Regards.