MATLAB
%%
T = 1;
N = 11;
np = 2;
dt = 0.001;
tmax = np*T;
t = -tmax:dt:tmax;
%% Function 1
%the following code was used to create the x(t) function
xrange = floor((T/dt)/15);
x1 = linspace(0,1,xrange);
x2 = x1(end-1:-1:1);
x3 = linspace(0,2,2*xrange);
x4 = x3(end-1:-1:1);
x5 = zeros(1,xrange);
x6 = x1;
x7 = 2*ones(1,xrange);
x8 = 1+x2;
x9 = -0.5*ones(1,xrange);
x10 = x1/2-0.5;
xtemp = [x1 x2 x3 x4 x5 x6 x7 x8 x9 x10];
ztemp = zeros(1,floor(T/dt)-length(xtemp));
xtT = [ztemp xtemp];
tT = dt:dt:T;
xt = 0;
for nn = 1:np
xt = [xtT xt xtT];
end
plot(t,xt)
axis([-tmax tmax -1 3])
grid on
xlabel('Time(s)');
%%
% Determine ak coefficients for x(t)
% Plot the approximation of x(t) using ak coefficients for
|k|<=11
%% function 2
% x2(t) = sin(4*pi*t) 0<t<1/2
% x2(t) = 0 1/2<t<1
% x2(t) = x2(t+1)
% Determine ak coefficients for x2(t)
% Plot the approximation of x2(t) using ak coefficients for
|k|<=11
ANSWER:
Given that
Executable Code:
T = 1;
N = 11;
np = 2;
dt = 0.001;
tmax = np*T;
t = -tmax:dt:tmax;
%% Function 1
%the following code was used to create the x(t) function
xrange = floor((T/dt)/15);
x1 = linspace(0,1,xrange);
x2 = x1(end-1:-1:1);
x3 = linspace(0,2,2*xrange);
x4 = x3(end-1:-1:1);
x5 = zeros(1,xrange);
x6 = x1;
x7 = 2*ones(1,xrange);
x8 = 1+x2;
x9 = -0.5*ones(1,xrange);
x10 = x1/2-0.5;
xtemp = [x1 x2 x3 x4 x5 x6 x7 x8 x9 x10];
ztemp = zeros(1,floor(T/dt)-length(xtemp));
xtT = [ztemp xtemp];
tT = dt:dt:T;
xt = 0;
for nn = 1:np
xt = [xtT xt xtT];
end
plot(t,xt)
axis([-tmax tmax -1 3])
grid on
xlabel('Time(s)');
%%
% Determine ak coefficients for x(t)
% Plot the approximation of x(t) using ak coefficients for
|k|<=11
%% function 2
% x2(t) = sin(4*pi*t) 0<t<1/2
% x2(t) = 0 1/2<t<1
% x2(t) = x2(t+1)
% Determine ak coefficients for x2(t)
% Plot the approximation of x2(t) using ak coefficients for
|k|<=11
Expected output:
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