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[[Image:hw2b1_moellerb_ECE301Fall2008mboutin.jpg|300px|frame|center|The continuous-time signal <math>x(t) = |2*cos(.5*t)|</math> is periodic.]] | [[Image:hw2b1_moellerb_ECE301Fall2008mboutin.jpg|300px|frame|center|The continuous-time signal <math>x(t) = |2*cos(.5*t)|</math> 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 <math>x[n] = |2*cos(.5*n)|</math> and is graphed below at a sampling rate of 1/7\pi | + | 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>. |
[[Image:hw2b2_moellerb_ECE301Fall2008mboutin.jpg|300px|frame|center|The discrete-time signal <math>x[n] = |2*cos(.5*n)|</math> is not periodic.]] | [[Image:hw2b2_moellerb_ECE301Fall2008mboutin.jpg|300px|frame|center|The discrete-time signal <math>x[n] = |2*cos(.5*n)|</math> is not periodic.]] | ||
Revision as of 15:58, 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.
