Generate half sine in matlab - matlab

Question

I have half a sine with time 0:2*T:
Rc = 1e3;
T = 1/Rc;
Fs = 2e3; % sampling frequency
dt = 1/Fs;
over = Fs/Rc; % sampling factor - 2
sps = 10;
time = 0:dt/sps:2*T;
half_Sine = sin(pi*time/(2*T)).^3;
figure(1);
plot(time,half_Sine, 'b--o');
grid on
xlabel('time','FontSize',13);
ylabel('a(t)','FontSize',13);
But i need time -T/2<= time<= T/2. And represent the time axis as time/T. When i do
time = -T/2:dt/sps:T/2;
This gives me not half a sine.
So I need something like this:

Answer 1

1.- the cube on the sin function prevents the resulting plot from having y axis symmetry.
Rc = 1e3;
T = 1/Rc;
Fs = 2e3; % sampling frequency
dt = 1/Fs;
over = Fs/Rc; % sampling factor - 2
sps = 10;
t =-2*T :dt/sps:2*T;
y= sin(pi*t/(2*T)).^3;
figure;
plot(t,y, 'b--o');
grid on
xlabel('time','FontSize',13);
ylabel('a(t)','FontSize',13);
2.- To have max on t=0 you need to use cos function , not sin,
and square, not cube
Rc = 1e3;
T = 1/Rc;
Fs = 2e3; % sampling frequency
dt = 1/Fs;
over = Fs/Rc; % sampling factor - 2
sps = 10;
t =-T :dt/sps:T;
y= cos(pi*t/(2*T)).^2;
figure(1);
plot(t,y, 'b--o');
grid on
xlabel('time','FontSize',13);
ylabel('a(t)','FontSize',13);
Now you have [-T T] plot,
3.- the interval you need is [-T/2 T/2]
t = -T/2:dt/sps:T/2;
y= cos(pit/(2T)).^2;
figure;
plot(t,y, 'b--o');
grid on
xlabel('time','FontSize',13);
ylabel('a(t)','FontSize',13);
4.- You mention you want to normalise the time axis.
If you modify t dividing by T the resulting plot is going to be a really narrow time span around t=0 and nearly constant y=1.
Instead, just modify the x axis anotation in the following way
figure;
hp1=plot(t,y, 'b--o');
hp1.XData=hp1.XData/T
grid on
xlabel('time/T','FontSize',13);
ylabel('a(t)','FontSize',13);