%question5%

function y = piecex2(n)
F = 0.1;
a = length(n);

for i = 1:a
    
    if -1/(2*F) <= n(i) & n(i) <= 1/(2*F) 
        y(i) = cos(2*pi*F*n(i));
    else
        y(i) = 0;
    end
end



%write this in command window%

F=0.1;
n=-1/(2*F)*5:1/(2*F)*5;

stem(n,piecex2(n))



%question6%

* first define impulse function and save it:

impulse function:

function y=impulse(t)

y=(t==0);


discrete impulse function:

function y = impDT(n)
    y = zeros(size(n));  % Initialize y as a numeric array
    
    % Define impulse function
    y(n == 0) = 1;

    % Find non-integer values of n
    ss = find(round(n) ~= n);
    
    % If there are non-integer values, replace corresponding elements in y with NaN
    if(~isempty(ss))
        y(ss) = NaN;
    end
end


%write this code in command window%

t=-10:0.001:10;
td=-10:10;

xt=impulse(t-2);
yn=impDT(td-5);

subplot(2,1,1)
plot(t,xt)
subplot(2,1,2)
stem(td,yn)



%question7%

%write this function in m-file and save it as piecex.m%

function y=piecex(t)

a=length(t);

for i=1:a

if -1<=t(i) & t(i)<=0
y(i)=(-1*t(i))+1;

elseif 0<=t(i) & t(i)<=1
y(i)=t(i)+1;

else
y(i)=0;

end
end

%write this in command window%

t=-8:0.1:8;

subplot(5,1,1)
plot(t,piecex(t),'g')
subplot(5,1,2)
plot(t,piecex(t-5),'m')
subplot(5,1,3)
plot(t,piecex(t+5),'y')
subplot(5,1,4)
plot(t,piecex(2*t-4),'r')
subplot(5,1,5)
plot(t,-2.*(piecex(-2*t+5)),'b')