(New page: == Periodic Signals and Non-Periodic Signals == Most of the signals from Homework 1 were boring (including mine) so I thought I'd broaden the periodic signal pool. I chose the CT signal:...) |
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Most of the signals from Homework 1 were boring (including mine) so I thought I'd broaden the periodic signal pool. | Most of the signals from Homework 1 were boring (including mine) so I thought I'd broaden the periodic signal pool. | ||
| − | I chose the CT signal: x(t) = |2*cos(.5*t)| . A graph of this signal in continuous time is shown below. | + | I chose the CT signal: <math>x(t) = |2*cos(.5*t)|</math> . A graph of this signal in continuous time is shown below. |
| − | [[ | + | [[Image:hw2b1_moellerb_ECE301Fall2008mboutin.jpg|300px|frame|center|The continuous-time signal <math>x(t) = |2*cos(.5*t)|</math> is periodic.]] |
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| + | As can be seen below, when the function mentioned earlier is sampled at the inappropriate frequency, the signal becomes non periodic. This function can be represented by <math>x[n] = |2*cos(.5*n)|</math> and is graphed below at a sampling rate of <math>1/7\pi</math>. | ||
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| + | [[Image:hw2b3_moellerb_ECE301Fall2008mboutin.jpg|300px|frame|center|The discrete-time signal <math>x[n] = |2*cos(.5*n)|</math> is not periodic.]] | ||
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| + | In addition to this observation, however, it is important to note that if several different time-shifted portions of this equation were laid on top of each other infinitely many times, it would become a periodic signal again. This is illustrated below. | ||
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| + | [[Image:hw2b4_moellerb_ECE301Fall2008mboutin.jpg|300px|frame|center|The discrete-time signal <math>x[n] = |2*cos(.5*n)|</math> becomes periodic when superimposed with several time-shifted iterations of itself.]] | ||
Latest revision as of 17:25, 11 September 2008
Periodic Signals and Non-Periodic Signals
Most of the signals from Homework 1 were boring (including mine) so I thought I'd broaden the periodic signal pool. I chose the CT signal: $ x(t) = |2*cos(.5*t)| $ . A graph of this signal in continuous time is shown below.
The continuous-time signal $ x(t) = |2*cos(.5*t)| $ is periodic.
As can be seen below, when the function mentioned earlier is sampled at the inappropriate frequency, the signal becomes non periodic. This function can be represented by $ x[n] = |2*cos(.5*n)| $ and is graphed below at a sampling rate of $ 1/7\pi $.
The discrete-time signal $ x[n] = |2*cos(.5*n)| $ is not periodic.
In addition to this observation, however, it is important to note that if several different time-shifted portions of this equation were laid on top of each other infinitely many times, it would become a periodic signal again. This is illustrated below.
The discrete-time signal $ x[n] = |2*cos(.5*n)| $ becomes periodic when superimposed with several time-shifted iterations of itself.
