Help Making a Piecewise Function Periodic

So I am trying to plot a piecewise function where z(t) = {t , 0 <= t < 1

e^(-5(t-1)) , 1 <= t < 2.5

0 , else

When I run it, it just gives the one period even though mod(t,2.5) should be keeping everything OK. How do I fix this? (I want to make it periodic)

(Oh yeah, my interval is -2 <= t <= 12)

t1 = -2 : 0.01 : 12; 
syms t z(t); % defining a symbolic variable
z(t) = (piecewise((mod(t,2.5)>=0)&(mod(t,2.5)<1),t, (mod(t,2.5)>=1)&(mod(t,2.5)<2.5), exp(-5.*(t-1)), 0));
z1 = z(t1);
figure
hold on
plot(t1, z1);

Answer 1

[Paul]

HI Connor,

Something like this?

syms t real
z(t) = piecewise(0 <= t <= 1,t, 1 < t <= 2.5, exp(-5*(t-1)),0);
fplot(z(t),[-2 12])

z1(t) = z(mod(t,2.5));
fplot(z1(t),[-2 12])

tval = -2:.01:12;
plot(tval,z1(tval))

[Walter Roberson]

Note by the way that piecewise is the only function that permits using 0 <= t <= 1 kind of syntax at the user level (at least that I can think of.)

(There are some symbolic functions that can return those structures.)

[Paul]

Also, bear in mind that that even though z1(t) is periodic, it is not the periodic extension of z(t). Rather z1(t) is the periodic extension of the product of z(t) and a rectangular window from t = 0 to t = 2.5.

[Anoop Kiran]

Hi Paul,

I tried your code, unfortunately it doesn't result in the periodic behavior at every 2.5 interval like the second and third plots that you have.

[Paul]

You'll need to show the exact code you ran and the results obtained before going any further.