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| + | [[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"]] | ||
| + | ---- | ||
== The Signal == | == The Signal == | ||
mmm lets randomly take... | mmm lets randomly take... | ||
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<math>\frac{1}{2j}(e^{j4\pi t}-e^{-j4\pi t}) + \frac{1}{2}(e^{j3\pi t} + e^{-j3\pi t}) + e^{j2\pi t}</math> | <math>\frac{1}{2j}(e^{j4\pi t}-e^{-j4\pi t}) + \frac{1}{2}(e^{j3\pi t} + e^{-j3\pi t}) + e^{j2\pi t}</math> | ||
| + | |||
| + | The terms come out to be | ||
| + | |||
| + | <math>4, -4, 3, -3, and 2</math> | ||
| + | |||
| + | <math>a_4 = \frac{1}{2j}</math> | ||
| + | <math>a_-4 = \frac{1}{2j}</math> | ||
| + | <math>a_3 = \frac{1}{2}</math> | ||
| + | <math>a_-3 = \frac{1}{2}</math> | ||
| + | <math>a_2 = 1</math> | ||
| + | |||
| + | <math>a_k = 0, k \ne 4, -4, 3, -3, 2</math> | ||
| + | |||
| + | ---- | ||
| + | [[Signals_and_systems_practice_problems_list|Back to Practice Problems on Signals and Systems]] | ||
Latest revision as of 10:03, 16 September 2013
Example of Computation of Fourier series of a CT SIGNAL
A practice problem on "Signals and Systems"
The Signal
mmm lets randomly take...
$ \sin4\pi t + \cos3\pi t + e^{j2\pi t} $
The Coefficients
Remeber... $ x(t) = \sum^{\infty}_{k = -\infty} a_k e^{jk\pi t}\, $
$ a_k=\frac{1}{T} \int_0^Tx(t)e^{-jk\omega_ot}dt $
Going to conver the equation into signal that is all in exponentials.
$ \frac{1}{2j}(e^{j4\pi t}-e^{-j4\pi t}) + \frac{1}{2}(e^{j3\pi t} + e^{-j3\pi t}) + e^{j2\pi t} $
The terms come out to be
$ 4, -4, 3, -3, and 2 $
$ a_4 = \frac{1}{2j} $ $ a_-4 = \frac{1}{2j} $ $ a_3 = \frac{1}{2} $ $ a_-3 = \frac{1}{2} $ $ a_2 = 1 $
$ a_k = 0, k \ne 4, -4, 3, -3, 2 $
