# What is the value of the given periodic signal at any time, how to solve it in MATLAB?

Firstly hello all, I need help about periodic signals. I have a question as below.

$$x(t)$$ is a periodic signal and $$0.1t^3[u(t) - u(t - 7)]$$ describes its one period.

What is the value of $$x(t)$$ at time $$t = 317$$?

Hint: Determine one period of the signal and find its values.

How can we solve this in MATLAB ? I tried with the code below, but answer was not correct

x(t) = 0.1 * t^3 * (heaviside(t) - heaviside(t - 7));
ezplot(x);
x(317)


Thank you.

Assuming continuous-time for the probem, for all periodic signals with a period of $$T$$ , for any integer $$m$$ , we have :

$$x( t + mT) = x(t) \tag{1}$$

So, for example with $$T=7$$ , and $$m=2$$ , you can see that $$x(15) = x(2\cdot 7 + 1) = x(1)$$. The operator that is used to find base argument for a given $$t$$ value is the modulus :

$$x(t) = x( \text{mod}(t,T) ) \tag{2}$$

where $$\text{mod}(t,T)$$ is the modulus of $$t$$ wrt $$T$$.

For your example, your period is $$T=7$$, and you can see that $$x(315) = x( \text{mod}(315,7) ) = x(2)$$.

Hence the value of $$x(t)$$ for $$t=2$$ is $$0.1 \cdot 2^3 = 0.8$$.

I don't know if there's anything to solve with MATLAB here though?