HW2-A Ben Horst ECE301Fall2008mboutin - Rhea

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Homework 2 Ben Horst: A  :: B  :: C  :: D  :: E

Part 1

The function I chose (at random) from homework1 can be found here.

The function x(t) = cos(t) is periodic in CT, as its period is 2$ \pi $. However, it is not periodic in DT.

Here is the function sampled at a frequency of 5 samples/unit:

cos(t) sampled at 5 per unit

The sampling shown based on index

Here is the function sampled at $ {\pi \over 2} $ (as closely as MATLAB is able to approximate pi)

cos(t) shown sampled at pi/2 per unit

The sampling shown based on index

Notice that the first image of values (from the first sampling) are not periodic. There is no integer 'N' such that sampling(n) = sampling(n+N). However, in the second case, this does occur. One may observe that sampling(n) = sampling(n+10). Thus, the second case is periodic.

Part 2

Another non-periodic function taken at random (found here) is log(x).

In order to form a periodic signal, we can take a section of a non-periodic function and repeat it on to infinity to form a periodic function.

Take for example the following MATLAB code that will repeat a section of log(x):

delta = .0001;
period = 5;
repetitions = 5;

t = [delta:delta:period];
a = log(t);
c = [];
for i=1:repetitions
   c = [c,a];
end
t = [delta:delta:period*repetitions];
plot(t,c)

Note that the code only repeats the function over a finite interval, it simply is meant to demonstrate how it this would be done.

The output of the MATLAB code shown above