%question1
%first write function in part a)

function y=xcon(t)

y=(exp(-2*t)).*(u(t)-u(t-4));

%write function in part b)

function y=xdis(n)

y=(exp(-n)).*(stepDT(n)-stepDT(n-4));

%periodic function of xcon

t=-150:150;
N=25;
periodicxcon=zeros(1,length(t));

for k=-5:5
periodicxcon=periodicxcon+xcon(t-k*N);
end

plot(t,periodicxcon)


%periodic function of xdis

n=-150:150;
N=25;
periodicxdis=zeros(1,length(n));

for k=-5:5
periodicxdis=periodicxdis+xdis(n-k*N);
end

stem(n,periodicxdis)

%energy of xcon

t=-10:10;
xcon_square=(xcon(t)).^2;
energy=trapz(t,xcon_square);
disp('energy of the signal is: ');
disp(energy);

%energy of xdis


n=-10:10;
xdis_square=(xdis(n)).^2;
energy=sum(xdis_square);
disp('energy of the signal is: ');
disp(energy);

%question2

%first define functions and plot them



%function in part a)

function y=xxa(n)

y=(cos((pi*n)/3)).*(stepDT(n)-stepDT(n-6));

%function in part b)

function y=xxb(n)

y=(((-1).^n)/3).*(stepDT(n));

%in the command window

n=-10:10;

subplot(2,1,1)
stem(n,xxa(n),'g')
subplot(2,1,2)
stem(n,xxb(n),'m')

%energy of xxa, notice that energy stays same
% as range of n is increased

n=-9000:9000;
xxa_square=(xxa(n)).^2;
xxa_energy=sum(xxa_square);
disp('energy of xxa is: ');
disp(xxa_energy);


%energy of xxb, notice that energy becomes infinite when 
%range of n is increased

n=-9000:9000;
xxb_square=(xxb(n)).^2;
xxb_energy=sum(xxb_square);
disp('energy of xxb is: ');
disp(xxb_energy);


% question3

%first, define and plot the functions
%function in part a)

function y = stepDT(n)
y = (n >= 0);
ss = find(round(n)~= n);
%F ind noninteger values of n
if(~isempty(ss))
y(ss) = NaN;
end

%function in part b)

function y=xx3b(n)

y=(-1).^n;

%function in part c)

function y=xx3c(n)

y=exp((-j*pi*n)/2);

%let's plot the signals

n=-50:50;

subplot(3,1,1)
stem(n,unitstepDT(n),'g')
subplot(3,1,2)
stem(n,xx3b(n),'m')
subplot(3,1,3)
stem(n,xx3c(n),'y')

%power of the first signal, notice that energy becomes infinity
%when range of n is increased


n=-1000:1000;
unitstepDT_square=(unitstepDT(n)).^2;
energy=sum(unitstepDT_square);
power=energy/length(n);
disp (['energy is: ',num2str(energy)]);
disp (['power is: ',num2str(power)]);


%power of signal xx3b, notice that energy becomes infinity
%when range of n is increased


n=-1000:1000;
xx3b_square=(xx3b(n)).^2;
energy=sum(xx3b_square);
power=energy/length(n);
disp (['energy is: ',num2str(energy)]);
disp (['power is: ',num2str(power)]);

%power of signal xx3c, notice that energy becomes infinity
%when range of n is increased and also notice that we take
%the square of magnitude because signal is complex


n=-1000:1000;
xx3c_square=(abs(xx3c(n))).^2;
energy=sum(xx3c_square);
power=energy/length(n);
disp (['energy is: ',num2str(energy)]);
disp (['power is: ',num2str(power)]);


% question4

%first define functions

function y=gncomplex(n)
y=abs((j/4).^n).*stepDT(n);


%in the command window

n=-20:20;

evenpart=(gncomplex(n) + gncomplex(-n))/2;
oddpart=(gncomplex(n) - gncomplex(-n))/2;

subplot(3,1,1)
stem(n,evenpart,'r')
subplot(3,1,2)
stem(n,oddpart,'k')
subplot(3,1,3)
stem(n,evenpart+oddpart,'b')

ne=-100:100;
energy_even=sum(((gncomplex(ne) + gncomplex(-ne))/2).^2);
disp('Energy of the even part is: ')
disp(energy_even)
energy_odd=sum(((gncomplex(ne) - gncomplex(-ne))/2).^2);
disp('Energy of the odd part is: ')
disp(energy_odd)
energy=sum((gncomplex(ne)).^2);
disp('Energy of the signal is: ')
disp(energy)
disp('Energy of the even+odd is: ')
disp(energy_even+energy_odd)

% question5

%first define signal function
function y=xk(k)
y = sinc(k/2) .* exp(-j*(2*pi*k)/4);  

%in the command window
n=-100:100;
xk_square=(abs(xk(n))).^2;
xk_energy=sum(xk_square);
disp('energy of xk is: ');
disp(xk_energy)