Proyek Akhir Sinyal-Sistem

function [output] = proyek(string)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% SISTEM DISKRIT %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
string = strrep(string, 'n', 't');
string = strrep(string, '[', '(');
string = strrep(string, ']', ')');


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% UJI LINEARITY %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
syms t;
syms a;
syms b;

% jika y1(t) = ax1(t), dimana x1(t) = t
x = @(t) a*t;
y1 = eval(string);

% jika y2(t) = bx2(t), dimana x2(t) = t^2
x = @(t) b*(t^2);
y2 = eval(string);

% jika y3(t) = ax1(t) + bx2(t)
x = @(t) (a*t) + (b*(t^2));
y3 = eval(string);

% membandingkan y3(t) dengan y1(t) + y2(t)
% substitusi t dengan angka arbitrary untuk membandingkan kedua hasil
if (subs(y3, t, 35) == subs(y1 + y2, t, 35)) 
	display('Sistem linear.');
	linear = true;
else
	display('Sistem tak linear.');
	linear = false;
end



%%%%%%%%%%%%%%%%%%%%%%%%%%%% UJI TIME-INVARIANCE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% jika y1(t) = x1(t), dimana x1(t) = t
x = @(t) t;
y1 = eval(string);

% jika y1(t) digeser menjadi y1(t-t0), dimana nilai t0 arbitrary
y1geser = subs(eval(string), t, (t-3));

% jika y2(t) = x1(t-t0), nilai t0 arbitrary
x = @(t) t-3;
y2 = eval(string);

% membandingkan apakah y2(t) = y1(t-t0)
% substitusi t dengan angka arbitrary untuk membandingkan kedua hasil 
if (subs(y2, t, 15) == subs(y1geser, t, 15))
	display('Sistem time-invariant.');
	ti = true;
else
	display('Sistem time-varying.');
	ti = false;
end

if (linear && ti)
	display('Sistem LTI.');
else
	display('Bukan sistem LTI.');
end

display(' ');
display(' ');