(New page: == Signal == Compute the Fourier series coefficients of the following signal: <font size=4><math>x(t) = 3cos(7t) + 11sin(4t)</math></font> == Fourier series == <font size=4><math>x(...) |
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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"]] | ||
| + | ---- | ||
== Signal == | == Signal == | ||
Compute the Fourier series coefficients of the following signal: | Compute the Fourier series coefficients of the following signal: | ||
| − | + | <math>x(t) = 3cos(7t) + 11sin(4t)\!</math> | |
| − | + | ||
== Fourier series == | == Fourier series == | ||
| − | + | <math>x(t) = 3cos(7t) + 11sin(4t)\!</math> | |
| − | + | ||
<math>x(t) = 3\frac{e^{i7t}+ e^{-i7t}}{2} + 11\frac{e^{i4t}- e^{-i4t}}{2i}</math> | <math>x(t) = 3\frac{e^{i7t}+ e^{-i7t}}{2} + 11\frac{e^{i4t}- e^{-i4t}}{2i}</math> | ||
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== Coefficients == | == Coefficients == | ||
| − | + | <math>w_0=1\!</math> | |
| − | + | ||
<math>a_4= \frac{11}{2i}</math> | <math>a_4= \frac{11}{2i}</math> | ||
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<math>a_7=a_{-7}= \frac{3}{2}</math> | <math>a_7=a_{-7}= \frac{3}{2}</math> | ||
| − | + | <math>a_k = 0\!</math> for all other <math>k \in \mathbb{Z}</math> | |
| + | ---- | ||
| + | [[Signals_and_systems_practice_problems_list|Back to Practice Problems on Signals and Systems]] | ||
Latest revision as of 10:04, 16 September 2013
Contents
Example of Computation of Fourier series of a CT SIGNAL
A practice problem on "Signals and Systems"
Signal
Compute the Fourier series coefficients of the following signal: $ x(t) = 3cos(7t) + 11sin(4t)\! $
Fourier series
$ x(t) = 3cos(7t) + 11sin(4t)\! $
$ x(t) = 3\frac{e^{i7t}+ e^{-i7t}}{2} + 11\frac{e^{i4t}- e^{-i4t}}{2i} $
$ x(t) = \frac{3}{2}e^{i7t}+ \frac{3}{2}e^{-i7t} + \frac{11}{2i}e^{i4t}- \frac{11}{2i}e^{-i4t} $
Coefficients
$ w_0=1\! $
$ a_4= \frac{11}{2i} $
$ a_{-4}= -\frac{11}{2i} $
$ a_7=a_{-7}= \frac{3}{2} $
$ a_k = 0\! $ for all other $ k \in \mathbb{Z} $
