| (15 intermediate revisions by one other user not shown) | |||
| Line 1: | Line 1: | ||
| + | [[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"]] | ||
| + | ---- | ||
==Periodic CT Signal== | ==Periodic CT Signal== | ||
| − | <math>x(t) = cos(3\pi t+\pi) \!</math> with fundamental frequency of \pi | + | <math>x(t) = cos(3\pi t+\pi) \!</math> with fundamental frequency of <math>\pi</math> |
| − | |||
| − | |||
| − | + | <math>x(t) = \frac{e^{j(3\pi t+\pi)}+e^{-j(3\pi t+\pi)}}{2}</math> | |
| − | <math> | + | |
| − | <math> | + | <math> = \frac{e^{j3\pi t}e^{\pi}+e^{-j3\pi t}e^{\pi}}{2}</math> |
| + | |||
| + | <math> = \frac{-e^{j3\pi t}-e^{-j3\pi t}}{2}</math> | ||
| + | |||
| + | <math> = -\frac{1}{2}e^{j3\pi t}-\frac{1}{2}e^{-j3\pi t}</math> | ||
| + | |||
| + | |||
| + | ==Fourier Series Coefficients== | ||
| + | <math>a_3 = -\frac{1}{2}</math> | ||
| − | <math> | + | <math>a_{-3} = -\frac{1}{2}</math> |
| + | ---- | ||
| + | [[Signals_and_systems_practice_problems_list|Back to Practice Problems on Signals and Systems]] | ||
Latest revision as of 10:08, 16 September 2013
Example of Computation of Fourier series of a CT SIGNAL
A practice problem on "Signals and Systems"
Periodic CT Signal
$ x(t) = cos(3\pi t+\pi) \! $ with fundamental frequency of $ \pi $
$ x(t) = \frac{e^{j(3\pi t+\pi)}+e^{-j(3\pi t+\pi)}}{2} $
$ = \frac{e^{j3\pi t}e^{\pi}+e^{-j3\pi t}e^{\pi}}{2} $
$ = \frac{-e^{j3\pi t}-e^{-j3\pi t}}{2} $
$ = -\frac{1}{2}e^{j3\pi t}-\frac{1}{2}e^{-j3\pi t} $
Fourier Series Coefficients
$ a_3 = -\frac{1}{2} $
$ a_{-3} = -\frac{1}{2} $
