My teacher assigned me a problem involving a discrete periodic function and I'm a little confused on how to solve.
Here is what was assigned (I paraphrased/summarized a bit):
For the given function sin((2f/fs)∙n∙T) find the integer value of T>1 such that the function is a periodic discrete signal. (multiple possible answers)
Variables given: f = 32 Hz, fs = 200
Part of the assignment involved using MATLAB to plot the function, which I think I managed to figure out. I ended up finding that a value of T=13 was a possible integer value which made the function a periodic discrete signal
The problem I have is I don't know how to mathematically explain why a value of T=13 works.
I tried to find a formula but I'm not sure how to apply it for my case, nor am I able to figure out any other values of T.
Does anyone know how I can either explain why T=13 works, or provide me a formula to find a more correct answer?
Note: I am really unfamiliar with signal stuff at all this was an assignment given in a class called "advanced engineering mathematics" which usually covers more differential equation stuff so if there are different tags or a different forum I should use pls let me know lol