Part A
The periodic signal I used in Part A was $ y=sin(x) $.
To create a DT signal from the above periodic CT signal I first sampled at an integer frequency of 1. The result was a non-periodic function.
This plot was the result of sampling the CT signal with frequency 1. The squares are the sampled points.
It is easily seen that when sampled at this frequency the resulting DT signal is non-periodic.
To create a periodic DT signal of this function, I then sampled the original CT signal at $ \pi \over 8 $.
This plot was the result of sampling the CT signal with frequency $ \pi \over 8 $. The sampled data points are represented by squares on the plot.
When the original CT signal is sampled at $ \pi \over 8 $ it is now a periodic DT function.
Part B
The signal I used to transform into a periodic function was $ y=e^x $.
I did this in MATLAB using the following code:
t = [.01:.01:5]; func = exp(t); y = []; for lcv=1:4 y = [y,func]; end t = [.01:.01:20]; plot(t,y)
What this does is repeats the function with a period of 5, and creates 4 full periods.
