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Sampling this signal at every integer time yields something altogether different. | Sampling this signal at every integer time yields something altogether different. | ||
| − | [[Image:hw2a1b_blaskows_ECE301Fall2008mboutin.jpg|frame|center| | + | [[Image:hw2a1b_blaskows_ECE301Fall2008mboutin.jpg|frame|center|300px|Sampling the continuous-time signal <math>x(t)=sin(t)</math> at integer times yields something like this. Note that the new discrete-time function <math>x[n]=sin(n)</math> is not periodic. Here we have shown five cycles of the formerly-periodic continuous time function.]] |
The new discrete time function looks like this on its own. | The new discrete time function looks like this on its own. | ||
| − | [[Image:hw2a1c_blaskows_ECE301Fall2008mboutin.jpg|frame|center| | + | [[Image:hw2a1c_blaskows_ECE301Fall2008mboutin.jpg|frame|center|300px|The non-periodic discrete-time function <math>x[n]=sin(n)</math>.]] |
Revision as of 06:45, 9 September 2008
Part 1
One can take a signal that would be periodic in continuous time and turn it into a signal that is not periodic in discrete time. Consider the continuous time signal $ x(t)=sin(t) $. Plotting this signal yields a smooth waveform that repeats itself with period $ T=2\pi $.
The continuous-time signal $ x(t)=sin(t) $ is periodic.
Sampling this signal at every integer time yields something altogether different.
Sampling the continuous-time signal $ x(t)=sin(t) $ at integer times yields something like this. Note that the new discrete-time function $ x[n]=sin(n) $ is not periodic. Here we have shown five cycles of the formerly-periodic continuous time function.
The new discrete time function looks like this on its own.
The non-periodic discrete-time function $ x[n]=sin(n) $.
