Code of Highpass filter for objective function in pso algorithm.

I am trying to design an optimal linear phase high pass filter using pso algorithm but it is giving me the graph for low pass filter.Can anyone please help me with the code for high pass filter to use as objective function.

The code I am currently using is:

function [o] = objFunction(x)

M = 10;

wc = 0.5 * pi;

hr = 0;

for i = 1:(M/2)

hr = hr + 2 * x(i) * cos(wc * ((M/2) - i));

h(i) = 1-(cos(wc * (M/2)) - 1i * sin(wc * (M/2)));

end

hr = hr + x(M/2);

e1 = abs(hr - h);

o = 20 * log10(hr);

end

Answer 1

[Pratyush Swain]

Hi Jayasree,

The issue that you are facing currently is your obejctive function seems to be set up for low-pass filter.

Your current expression for (h):

h(i) = 1-(cos(wc * (M/2)) - 1i * sin(wc * (M/2)));

This above uses a fixed angle, resulting in same values of h(i) which could be why your original filter response was not shaping properly.

To modify it for a high-pass filter, you can adjust the desired response (h) and the way you compute the error (e1). Please refer to following implementation:

function [o] = objFunction(x)
    M = 10; 
    wc = 0.5 * pi;
    hr = 0;
    h = zeros(1, M/2);

    % Calculate the actual filter response hr
    for i = 1:(M/2)
        hr = hr + 2 * x(i) * cos(wc * ((M/2) - i));
    end
    hr = hr + x(M/2);

    % Desired high-pass filter response
    for i = 1:(M/2)
        h(i) = -1 * (cos(wc * ((M/2) - i)) - 1i * sin(wc * ((M/2) - i)));
    end

    % Error between desired and actual response
    e1 = abs(hr - h);

    o = sum(e1);
end

Please note, for error calculation, you can also use the MSE(Mean Squared Error) as an alternative to absolute error.

Hope this helps