Question 1
I chose the signal $ x[n]=e^{j\pi n} \, $ which Jeff Kubascik posted on his HW1.
Recall that this signal is periodic if $ T = {\omega_0\over2\pi}\, $ is rational.
Say I choose the sampling period $ T_s=.1\, $
The output will be:
But if I choose the sampling period to be $ T_s=.7\, $
Question 2
I'm including the code for this part because I found help using Tyler Houlihan's work. He apparently also received help from Wei Jian Chan's HW. I used Tyler's code as a base to recreate a periodic signal from:
$ e^{-t}sin(t)\, $
Here's the code:
%Creating 3 time vectors t=[0:0.001:1.5;0:0.001:1.5;0:0.001:1.5]; %setting the three variables, with their offsets y =exp(-t(1,:)).*sin(t(1,:)); y2=exp(-t(2,:)).*sin(t(2,:)); y3=exp(-t(3,:)).*sin(t(3,:)); %concatenating them, ie putting them after another y4=[y,y2,y3]; %making the new time axis for the whole thing t=0:0.001:4.502; %plotting plot(t,y4);
and the plot
