(New page: ==Definition== x(t) is periodic if there existes T>0 such that x(t)=x(T+t)) |
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| − | ==Definition== | + | [[Category:problem solving]] |
| + | [[Category:ECE301]] | ||
| + | [[Category:ECE]] | ||
| + | [[Category:Fourier series]] | ||
| + | [[Category:signals and systems]] | ||
| + | == Example of Computation of Fourier series of a CT SIGNAL == | ||
| + | A [[Signals_and_systems_practice_problems_list|practice problem on "Signals and Systems"]] | ||
| + | ---- | ||
| + | |||
| + | ==Definition of Periodic CT Signal== | ||
x(t) is periodic if there existes T>0 such that x(t)=x(T+t) | x(t) is periodic if there existes T>0 such that x(t)=x(T+t) | ||
| + | |||
| + | ==Example== | ||
| + | |||
| + | Let's look at: <math>x(t)=3*cos(3t)</math>, we know that the fudamental period of x(t) is | ||
| + | |||
| + | <math>w_0=2\pi/T=3</math> | ||
| + | |||
| + | <math>x(t)=3cos(3t)</math> | ||
| + | |||
| + | <math>=\frac{3}{2}[(e^{j3t})+(e^{-j3t})]</math> | ||
| + | |||
| + | <math>=\frac{3}{2}(e^{j3t})+\frac{3}{2}(e^{-j3t})</math> | ||
| + | |||
| + | so we can see that when k=1, <math>a_1=\frac{3}{2}</math>, and when k=-1,<math>a_{-1}=\frac{3}{2}</math> | ||
| + | |||
| + | others are all zero | ||
| + | ---- | ||
| + | [[Signals_and_systems_practice_problems_list|Back to Practice Problems on Signals and Systems]] | ||
Latest revision as of 10:53, 16 September 2013
Example of Computation of Fourier series of a CT SIGNAL
A practice problem on "Signals and Systems"
Definition of Periodic CT Signal
x(t) is periodic if there existes T>0 such that x(t)=x(T+t)
Example
Let's look at: $ x(t)=3*cos(3t) $, we know that the fudamental period of x(t) is
$ w_0=2\pi/T=3 $
$ x(t)=3cos(3t) $
$ =\frac{3}{2}[(e^{j3t})+(e^{-j3t})] $
$ =\frac{3}{2}(e^{j3t})+\frac{3}{2}(e^{-j3t}) $
so we can see that when k=1, $ a_1=\frac{3}{2} $, and when k=-1,$ a_{-1}=\frac{3}{2} $
others are all zero
