(One intermediate revision 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"]]
 +
----
 
== The Signal ==
 
== The Signal ==
 
mmm lets randomly take...
 
mmm lets randomly take...
Line 26: Line 35:
  
 
<math>a_k = 0, k \ne 4, -4, 3, -3, 2</math>
 
<math>a_k = 0, k \ne 4, -4, 3, -3, 2</math>
<math>A_</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 $


Back to Practice Problems on Signals and Systems

Alumni Liaison

Ph.D. 2007, working on developing cool imaging technologies for digital cameras, camera phones, and video surveillance cameras.

Buyue Zhang