SS Lab Class No 7

%{
 SS Lab Class 7
 Rahat Sir
 Date: 06-11-2019
%}
% Solution of Differential Equation
%f = 'Dy + y - cos(t)';
%y = dsolve(f,'y(0)=2');
%ezplot(y,[1 20])
%f ='2*D2y+Dy+y-D(cos(t))';
% Evaluate difference Equation
b = [.067 .1349 .675];
a =[1 -1.143 .4128];
n = 1:20;
x = (.5).^n;
zi = filtic(b,a,[1 2]);

y = filter(b,a,x,zi);
stem
%% Fourier Series
T0 = 1; E =1; w0 = 2*pi; a0 =E/2;

n = 20;
f = a0/2;
t = -1.5:.01:1.5;

for N=1:n
     an = ((2*E)/(N*w0*T0))*(sin(N*pi/2)-sin(3*N*pi/2));
     f = f+ an .* cos(N*w0*t);
end

plot(t,f)

%f = a0/2 + sum(an*cos nwt)
%% another fourier Series
T0 = 2*pi; w0=1; a0=1/2; E = 1;
n =20;
f = a0/2;
t = -1.5:.01:1.5;

for N=1:n
    bn = -1/(n.*pi);
    f = f+ bn.*cos(N*wo*t);
end
plot(t,f)