laboration 2 - applied mathematics

lab2.m

startlab2;
whos;

% close all;
%% %%%%%%%%% 2.2
% plot the theta function (t > t_0 = 1, t < t_0 = 0)
%figure;plot(t, theta);


% plot the DeltaDirac-function (t = t_0 ==> 1, else 0)
%figure;plot(t, delta);

%figure
%plot(t, sin(t).*(t>0) + cos(t).*((5-t)>0));

%pause;
%close all;
%%%%%%%%%%%% end of 2.2

%% %%%%%%%%%%% 2.3
krekt = (t>0)-(t>1);
triangel = (t+1).*(t>-1)-2*t.*(t>0)+(t-1).*(t>1);
kcos = cos(t).*(t>0);

% figure; 
% hold on
% plot(t, krekt);
% plot(t, triangel);
% plot(t, kcos);
% hold off
% 
%% %%%%%%%%%%% 2.4
% pause;
% close all;
% y=lpfilter(theta);
% plot(t,y);
% 
%% %%%%%%%%%%% 2.5
% pause; close all;
% plotsyst('lpfilter',theta);

%% %%%%%%%%%% 2.6
% % pause; 
% % The one-wheeled car.
% % input signal f(t) = theta(t) represents the road height
% % output signal y = S*f(t) represents the cars position as height, viewed
% % in cross-section from the side, like in Super Mario.
% close all;
% plotsyst('bil',theta);

%% %%%%%%%%%% 2.7
% % In this model, the input signal is 
%  plotsyst('brygga', theta);
% % Svar: Ja, det tror jag. Eftersom y(t) = S(t)*f(t) borde vi ju kunna styra
% % hur utsignalen genom att styra R och C för att få den utsignal vi vill.
% % Det står även i kursboken att 

%% %%%%%%%%% 2.8
% % hold
% figure;
% subplot(2,2,1);
% 
% plot(t, delay(triangel, 2));
% title('triangel, 2 shift');
% xlabel('insignal');
% grid;
% 
% subplot(2,2,3);
% plot(t, delay(triangel, -3));
% xlabel('insignal');
% title('triangel, -3 shift');
% grid;
% 
% subplot(2,2,2);
% plot(t, delay(kcos, 2));
% title('kcos, 2 shift');
% xlabel('insignal');
% grid;
% 
% subplot(2,2,4);
% plot(t, delay(kcos, -3));
% title('kcos, -3 shift');
% grid;


%% %%%%%%%% 2.9
% figure;

% close all;
% plotsyst('differentiator', triangel);
% plotsyst('differentiator', krekt);
% plotsyst('differentiator', theta);
% plotsyst('differentiator', delta);
% plotsyst('differentiator', kcos);
% 
% % Svar: Spikarna kan representeras med hjälp av DeltaDirac-funktioner med
% % DeltaDirac(t - a) där spikarna uppstår.

%% %%%%%%% 2.11
% lintest('lpfilter', triangel, kcos, -3, 4);

%% %%%%%%%% 2.12
% plotsyst('lpfilter', triangel);
% plotsyst('lpfilter', delay(triangel, 2));
% plotsyst('lpfilter', delay(triangel, -3));
% delaytest('lpfilter', triangel, 2);
% delaytest('lpfilter', triangel, -3);
% delaytest('lpfilter', triangel, 1);

%% %%%%%%%%%% 2.14
% plotsyst('lpfilter', triangel + delay(triangel, -5) + delay(triangel, -15));

%% %%%%%%%%%% 2.15
% close all;

% lintest('syst1', theta, theta, 1,1);
% lintest('syst2', theta, theta, 1,1);
% lintest('syst3', theta, theta, 1,1); % Not linear?
% lintest('syst4', theta, theta, 1,1);
% lintest('syst5', theta, theta, 1,1);
% lintest('syst6', theta, theta, 1,1);
%
% lintest('syst1', theta,1-theta,1,1); % Not linear?
% lintest('syst2', theta,1-theta,1,1);
% lintest('syst3', theta,1-theta,1,1);
% lintest('syst4', theta,1-theta,1,1);
% lintest('syst5', theta,1-theta,1,1); % Not lienar? 
% lintest('syst6', theta,1-theta,1,1);

% How am I supposed to test linearity? It's not linear if for any 
% y(t) != 0?

%plotsyst('lpfilter', (1-theta));
close all;
% delaytest('syst1', triangel, 2);
% delaytest('syst1', triangel, -3);
% 
%  delaytest('syst2', triangel, 2);
%  delaytest('syst2', triangel, -13);
% % svar: Den här verkar ju INTE vara tidsvariant!!
% 
% delaytest('syst3', triangel, 2);
% delaytest('syst3', triangel, -13);
% 
% delaytest('syst4', triangel, 2);
% delaytest('syst4', triangel, -13);

% delaytest('syst5', triangel, 12);
% delaytest('syst5', triangel, -13);

% delaytest('syst6', triangel, 12);
% delaytest('syst6', triangel, -13);
% % svar: Den här verkar ju INTE vara tidsvariant!!

% delaytest('syst1', delta, 2);
% delaytest('syst1', delta, -3);
% delaytest('syst1', delta, 10);
% pause
% delaytest('syst2', delta, 2);
% delaytest('syst2', delta, -3);
% delaytest('syst2', delta, 10);
% pause
% delaytest('syst3', delta, 2);
% delaytest('syst3', delta, -3);
% delaytest('syst3', delta, 10);
% pause
% delaytest('syst4', delta, 2);
% delaytest('syst4', delta, -3);
% delaytest('syst4', delta, 10);
% pause
% delaytest('syst5', delta, 2);
% delaytest('syst5', delta, -3);
% delaytest('syst5', delta, 10);
% pause
% delaytest('syst6', delta, 2);
% delaytest('syst6', delta, -3);
% delaytest('syst6', delta, 10);

%% %%%%%%%%%%%%% 2.16
h = syst1(delta);
y = falt(h, triangel);
plotsyst('syst1', triangel);
figure;
subplot(211);
plot(t,y);