Hi Jacob,
Assuming that you do not want to use the inbuilt command for matched filter, here is the way to create signals, find the impulse response and get the signal output after passing through the matched filter.
% Input signal x(t)
rect1 = @(x,a) ones(1,numel(x)).*(abs(x)<a); % a is the width of the pulse
rect2 = @(x,a) -ones(1,numel(x)).*(abs(x)<a); % a is the width of the pulse
x = 1:1:1e4;
y1 = rect1(x,1e4);
y2 = rect2(x,1e4);
% Backward signal y1(-t), y2(-t)
newX = -1e4:1:-1;
newY1 = rect1(newX,1e4);
newY2 = rect2(newX,1e4);
figure(1)
subplot(2,1,1);
plot(x,y1,'c');
hold on;
plot(newX,newY1,'m');
subplot(2,1,2);
plot(x,y2,'c');
hold on;
plot(newX,newY2,'m');
% Impulse Response of matched filter y1(T-t)
% Shift the newY1 and newY2 to get the impulse response of y1 and y2
% Signal output after passing through the matched filter
% Convolute the shifted signal and y1 to get the filter output using conv. Similarly for y2.
For more information, refer the following links.
