Plotting 3 cycles of a periodic signal

Hi all,

Ive been trying to plot 3 cycles of the below function.

z(t) = ( t + 4 if − π ≤ t < 0,

e if 0 ≤ t ≤ π)

this is what ive wroten so far, i know all ive done is plot one cycle and then move it along x axis, but i would rather have another way of doing the same thing.

t0 = -pi:0.00001:pi;  
T0 = length(t0);
 
    for i = 1:T0
    if t0(i)< 0
        z0(i)=t0(i)+4;
    else
        z0(i)=exp(1);
    end
    end
    
t1 = -pi:0.00001:pi;
T1 = length(t1);
 
    for i = 1:T1
    if t1(i)< 0
        z1(i)=t1(i)+4;
    else
        z1(i)=exp(1);
    end
    end
    
t2 = -pi:0.00001:pi;
T2 = length(t2);
 
    for i = 1:T2
    if t2(i)< 0
        z2(i)=t2(i)+4;
    else
        z2(i)=exp(1);
    end
    end
    
figure;
plot(t0, z0, 'r');
hold on
plot(t1+2*pi, z1, 'b');
hold on
plot(t2+4*pi,z2, 'g');

[Walter Roberson]

That function is not periodic.

[John D'Errico]

When you delete your question, you insult those who made the effort, who spent the time to answer your questin. You hurt Answers itself, because nobody else can learn from the answer.

[Stephen23]

https://web.archive.org/web/20201103060715/https://webcache.googleusercontent.com/search?q=cache%3A0R_TlCO8hg8J%3Ahttps%3A%2F%2Fuk.mathworks.com%2Fmatlabcentral%2Fanswers%2F633289-plotting-3-cycles-of-a-periodic-signal

Original question by Samuel Courtney retrieved from Google Cache:

"Plotting 3 cycles of a periodic signal"

Hi all,

Ive been trying to plot 3 cycles of the below function.

z(t) = ( t + 4 if − π ≤ t < 0,

e if 0 ≤ t ≤ π)

this is what ive wroten so far, i know all ive done is plot one cycle and then move it along x axis, but i would rather have another way of doing the same thing.

t0 = -pi:0.00001:pi;  
T0 = length(t0);
 
    for i = 1:T0
    if t0(i)< 0
        z0(i)=t0(i)+4;
    else
        z0(i)=exp(1);
    end
    end
    
t1 = -pi:0.00001:pi;
T1 = length(t1);
 
    for i = 1:T1
    if t1(i)< 0
        z1(i)=t1(i)+4;
    else
        z1(i)=exp(1);
    end
    end
    
t2 = -pi:0.00001:pi;
T2 = length(t2);
 
    for i = 1:T2
    if t2(i)< 0
        z2(i)=t2(i)+4;
    else
        z2(i)=exp(1);
    end
    end
    
figure;
plot(t0, z0, 'r');
hold on
plot(t1+2*pi, z1, 'b');
hold on
plot(t2+4*pi,z2, 'g');

Answer 1

[Cris LaPierre]

No need to create the same values 3 times. Your code can be simplified to the following. You also don't need nearly as many points to create the visualization.

t0 = -pi:0.01:pi;  
T0 = length(t0);
 
for i = 1:T0
    if t0(i)< 0
        z0(i)=t0(i)+4;
    else
        z0(i)=exp(1);
    end
end

plot(t0, z0, 'r',t0+2*pi, z0, 'b',t0+4*pi,z0, 'g');

[Walter Roberson]

If you use this kind of code structure, then be careful about endpoints. If the period is exactly divisible by the increment, then you end up with a data point at initial + period due to the end point of the first period, and you end up with with a data point at the same location due to the starting point of the second period.

This particular code has a period of 2*pi which is not exactly divisible by 0.01 so the endpoint of the first period is slightly before the start point of the second period so you are saved.

[Walter Roberson]

syms t
Mod = @(A,B) A-floor(A/B)*B
z0 = piecewise(Mod(t, 2*pi)<=pi, exp(1), Mod(t, 2*pi)+4-2*pi)
fourier(z0)
Z0 = double(subs(z0, t, linspace(-pi,5*pi,257))) ;
Z0(end) = [] ;
FZ = fft(Z0) ;