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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.

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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?

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    $\begingroup$ Thanks for your answer :) $\endgroup$
    – user54398
    Dec 2 '20 at 13:24

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