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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). | 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. | However, in the second case, this does occur. One may observe that sampling(n) = sampling(n+10). Thus, the second case is periodic. | ||
Revision as of 10:05, 9 September 2008
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:
Here is the function sampled at $ {\pi \over 2} $ (as closely as MATLAB is able to approximate pi)
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.
