I'm preparing for a lab in a Signals and Systems course in my university, 5th semester.
I've found old exercise material from the class and since I know some Matlab and have dealt with LTI systems and impulse responses of signals before, I decided to try to tackle them.
Of course, I was completely wrong in my decision and I reached a dead-end.
Here's the first part of the exercise, graded for 50%:
The same sine signal $x(n)$ (of your choice) is inserted into two different Linera Time-invariant (LTI) systems with impulse response $h1(n) = u(n)$ and $h2(n) = u(n-10)$, accordingly.
$\alpha )$ Compare the two exits $y1(n)$ and $y2(n)$
$\beta )$ Are the exit signals periodical?
Some questions before my attempt, along with some of my code:
1: I decided to go for this sine-signal:
Fs=1; t=0:1/Fs:1000; x=sin(2*pi*0.01*t);
2: Does "are inserted" imply Convolution?
3: How can you mathematically check for periodicality apart from seeing the repetitions with your eye and calling it a day?