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[[Homework 2_ECE301Fall2008mboutin|<< Back to Homework 2]]
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Homework 2 Ben Horst:  [[HW2-A Ben Horst _ECE301Fall2008mboutin| A]]  ::  [[HW2-B Ben Horst _ECE301Fall2008mboutin| B]]  ::  [[HW2-C Ben Horst _ECE301Fall2008mboutin| C]]  ::  [[HW2-D Ben Horst _ECE301Fall2008mboutin| D]]  ::  [[HW2-E Ben Horst _ECE301Fall2008mboutin| E]]
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----
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==Part 1==
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The function I chose (at random) from homework1 can be found [[HW1.4 Miles Whittaker - Periodic and Non-Periodic Examples _ECE301Fall2008mboutin| here]].
 
The function I chose (at random) from homework1 can be found [[HW1.4 Miles Whittaker - Periodic and Non-Periodic Examples _ECE301Fall2008mboutin| here]].
  
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[[Image:hw2_1_A1_ECE301Fall2008mboutin.png|frame|left|100px|...caption1...]][[Image:hw2_1_A2_ECE301Fall2008mboutin.png|frame|right|100px|...caption2...]]
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[[Image:hw2_1_A1_ECE301Fall2008mboutin.png|thumb|left|300x300px|cos(t) sampled at 5 per unit]]
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[[Image:hw2_1_A2_ECE301Fall2008mboutin.png|thumb|right|300x300px|The sampling shown based on index]]
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[[Image:hw2_1_A3_ECE301Fall2008mboutin.png|frame|left|100px|...caption3...]][[Image:hw2_1_A4_ECE301Fall2008mboutin.png|frame|right|100px|...caption4...]]
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[[Image:hw2_1_A3_ECE301Fall2008mboutin.png|thumb|left|300x300px|cos(t) shown sampled at pi/2 per unit]]
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[[Image:hw2_1_A4_ECE301Fall2008mboutin.png|thumb|right|300x300px|The sampling shown based on index]]
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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).
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However, in the second case, this does occur. One may observe that sampling(n) = sampling(n+10). Thus, the second case is periodic.
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==Part 2==
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Another non-periodic function taken at random (found [[HW1.4 Sean Ray _ECE301Fall2008mboutin| here]]) is log(x).
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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.
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Take for example the following MATLAB code that will repeat a section of log(x):
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<pre>
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delta = .0001;
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period = 5;
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repetitions = 5;
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t = [delta:delta:period];
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a = log(t);
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c = [];
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for i=1:repetitions
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  c = [c,a];
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end
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t = [delta:delta:period*repetitions];
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plot(t,c)
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</pre>
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Note that the code only repeats the function over a finite interval, it simply is meant to demonstrate how it this would be done.
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[[Image:hw2_A2_bhorst_ECE301Fall2008mboutin.png|frame|center|The output of the MATLAB code shown above]]

Latest revision as of 06:59, 10 September 2008

<< Back to Homework 2

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

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