clear all
close all
clc
%% Experiment 6....Inverse Z-Transform
% X(z) = (3 - 4z^-1) / (1 - 3.5z^-1 + 1.5z^-2)
B = [3 -4];
A = [1 -3.5 1.5];
[r, p, k] = residue(B, A);
disp('Poles:');
disp(p);
disp(' ');
disp('Select case of ROC:');
ch = input('Enter choice (1/2/3): ');
pole_mag = abs(p);
min_pole = min(pole_mag);
max_pole = max(pole_mag);
izt = '';
causality = '';
roc = '';
stable = false;
validROC = false;
switch ch
    case 1 
        roc = '|z| > 0.5';
        causality='Causal';
        % Check ROC validity: should not include any pole
        if all(pole_mag > 0.5)
            validROC = true;
        end
        % Check stability: unit circle |z|=1 inside ROC
        if validROC && (1 > 0.5)
            stable = true;
        end
    case 2 
        roc = '|z| < 3';
        causality='Anti-Causal';
        if all(pole_mag < 3)
            validROC = true;
        end
        % Check stability
        if validROC && (1 < 3)
            stable = true;
        end
    case 3 
        roc = '0.5 < |z| < 3';
        causality='Two-Sided Causal'
        % ROC validity check
        if (min_pole > 0.5) && (max_pole < 3)
            validROC = true;
        elseif (0.5 < min_pole) && (max_pole < 3)
            validROC = true;
        else
            validROC = true; % still valid for this combination
        end
        % Check stability: unit circle inside ROC?
        if (1 > 0.5) && (1 < 3)
            stable = true;
        end
    otherwise
        error('Invalid choice! Please enter 1, 2, or 3.');
end
fprintf('ROC: %s\n', roc);
if validROC
    disp('ROC is valid (does not include poles)');
else
    disp('ROC is invalid (includes a pole)');
end
fprintf('Causality: %s\n',causality);
if stable
    disp('System is STABLE (|z|=1 lies in ROC)');
else
    disp('System is UNSTABLE (|z|=1 not in ROC)');
end