%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%% pp. 5 - 6  Creating and Plotting Functions of Time  %%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

t=0:0.01:5;   
y=3*(t.^2) + t + 5;
plot(t,y)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


t=-5:0.01:5;      
u=(t>=0); 
r=t.*u;

plot(t,r)

y=r.*sin(5*pi*t);

plot(t,y)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%


t=0:0.01:8;   
fo=1/2; 
s=sin(2*pi*fo*t);
plot(t,s)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%% p. 9  Matrix Rows containing separate functions of time  %%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
t=0:0.01:5;
x=t;
y=t.^2;
A=[x;y];
plot(t,A)   %

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%% p. 10  Summation  %%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

S=sum(1:10)

%%%%%
B=[1:10;10:19]
sum(B)

%%%%%
z=sum(A);
plot(t,z)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%% p. 10  Indexing  %%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


x=20:30
x(3)
x(1:2:11)
x(2:2:10)


x=1:3
y=(1:4)'  
B=y*x

z=B(2,:)

z=B(2,1:2)

z=B(:,3)


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%% p. 12  Looping  %%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
N=10;
for n=1:N
X1(n)=1/(n^2);
end

X1

%%%%%  vs.  Non-Looping  %%%%%

N=10;
n=1:N
X2=1./(n.^2);


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%% p. 13  Signals & Systems  %%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
del_t = 0.02e-3;
t=0:del_t:10e-3; % creates a 1 x 501 row vector of time points
n=(1:10).'; % creates a 10x1 column vector of integers 1 to 10
COS=cos((n*t)*2*pi*500);

plot(t,COS(1,:),'b')
hold on
plot(t,COS(2,:),'r--')
hold off


A=-5./(pi*n.^2)


size(A(:,ones(1,501)))
plot(t,A(1,:))
plot(t,A(2,:))

size(A(:,ones(1,501)).*COS)
B=A(:,ones(1,501)).*COS;
plot(t,B(1,:))

x=sum(A(:,ones(1,501)).*COS);
plot(t,x)