(New page: == HW4.1 == periodic signal: <math> \begin{align} x(t) = 32 + 8sin(2\pi t) + 22cos(2\pi t) + 2cos(2\pi t+\pi /2)\end{align} </math> re-writing the signal in the form of <math> \begin{alig...) |
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| + | [[Category:problem solving]] | ||
| + | [[Category:ECE301]] | ||
| + | [[Category:ECE]] | ||
| + | [[Category:Fourier series]] | ||
| + | [[Category:signals and systems]] | ||
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| + | == Example of Computation of Fourier series of a CT SIGNAL == | ||
| + | A [[Signals_and_systems_practice_problems_list|practice problem on "Signals and Systems"]] | ||
| + | ---- | ||
== HW4.1 == | == HW4.1 == | ||
periodic signal: <math> \begin{align} x(t) = 32 + 8sin(2\pi t) + 22cos(2\pi t) + 2cos(2\pi t+\pi /2)\end{align} </math> | periodic signal: <math> \begin{align} x(t) = 32 + 8sin(2\pi t) + 22cos(2\pi t) + 2cos(2\pi t+\pi /2)\end{align} </math> | ||
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\end{align}</math> | \end{align}</math> | ||
| + | ---- | ||
| + | [[Signals_and_systems_practice_problems_list|Back to Practice Problems on Signals and Systems]] | ||
Latest revision as of 11:05, 16 September 2013
Example of Computation of Fourier series of a CT SIGNAL
A practice problem on "Signals and Systems"
HW4.1
periodic signal: $ \begin{align} x(t) = 32 + 8sin(2\pi t) + 22cos(2\pi t) + 2cos(2\pi t+\pi /2)\end{align} $
re-writing the signal in the form of $ \begin{align} e^{jw_0t} \end{align} $ we get $ \begin{align} x(t) = 32 + \frac{8}{2j} \left ( e^{j 2 \pi t} - e^{-j 2 \pi t} \right ) + 11 \left ( e^{j 2 \pi t} + e^{-j 2 \pi t} \right ) + \left ( e^{j 2 \pi t + \pi /2 } + e^{-j 2 \pi t + \pi /2} \right ) \end{align} $
then we can convert these to the coefficients of the Fourier series
$ \begin{align} a_0 = 32 \\ a_1 = 11 - 4/j \\ a_{-1} = 11 + 4/j \\ a_2 = e^{ \pi /2} \end{align} $
