function [Z,P] = zeroPole(b,a,plt)

%{
function [Z,P] = zeroPoles(b,a,plt)
Ex: [Z,P] = zeroPoles([1 0.5 -1],[1 0 0.81],1)

Task: To compute the zeros and poles of a transfer function 

Inputs:
    -a: vector of a_i (denominator)
    -b: vector of b_i (numerator)
    -plt: plot if greater than 0

Outputs:
    -Z: zeros (roots of the numerator)
    -P: poles (roots of the denominator)

Author: Tikea TE
Date: 15/04/2025
%}

% ======== calculate the zeros =========
Z = roots(b);
% ======== calculate the poles =========
P = roots(a);

if(plt)
    figure;
    zplane(Z,P);
    title("zeros and poles of H(z) in the complex plane");
    xlabel("Real part");
    ylabel("imaginary part");
    legend("zeros","poles");
    grid on;

    figure;
    impz(b,a);
    title("Impulse response");
    xlabel("samples (n)");
    ylabel("amplitude of the output y")
    grid on;
end