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[[Category:ECE]] | [[Category:ECE]] | ||
[[Category:Fourier series]] | [[Category:Fourier series]] | ||
| − | + | [[Category:signals and systems]] | |
== Example of Computation of Fourier series of a CT SIGNAL == | == Example of Computation of Fourier series of a CT SIGNAL == | ||
A [[Signals_and_systems_practice_problems_list|practice problem on "Signals and Systems"]] | A [[Signals_and_systems_practice_problems_list|practice problem on "Signals and Systems"]] | ||
Latest revision as of 09:58, 16 September 2013
Example of Computation of Fourier series of a CT SIGNAL
A practice problem on "Signals and Systems"
Define a Periodic CT signal and compute its Fourier series coefficients
Consider the following CT signal:
x(t) such that
$ ak = \frac{1}{T} \int_{0}^{T} x(t) * e^{-j*k} * \frac{2*\pi}{T} *dt $
$ x(t) = cos(2* \pi * t) * cos(4* \pi * t) $
$ = \frac{e^{j*2*\pi*t} + e^{-j*2*\pi*t}}{2} $
$ = \frac{1*e^{j*6*\pi*t}}{4} + \frac{e^{-j*2*\pi*t}}{4} + \frac{e^{j*2*\pi*t}}{4} + \frac{e^{-j*6*\pi*t}}{4} $
K = 3
K= -1
K= 1
K= -3
$ a^{3} = \frac{1}{4} $
$ a^{-1} = \frac{1}{4} $
$ a^{1} = \frac{1}{4} $
$ a^{-3} = \frac{1}{4} $
