View source for Table of CT Fourier series coefficients and properties (include some computations and proofs if you are really brave) - Rhea

= Table of CT Fourier series coefficients and properties =

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::You may want to switch the titles of the second and third column. -pm
== Some Fourier series ==


{| border="1" class="wikitable"
|-
! Function 
! Fourier Series 
! Coefficients
|-
| <math>sin(w_0t)</math> 
| <math>\frac{1}{2j}e^{jw_0t}-\frac{1}{2j}e^{-jw_0t}</math> 
| <math>a_1=\frac{1}{2j}, a_{-1}=\frac{-1}{2j}, a_k=0 \mbox{ for } k \ne 1,-1</math>
|-
| <math>cos(w_0t)</math> 
| <math>\frac{1}{2}e^{jw_0t}+\frac{1}{2}e^{-jw_0t}</math> 
| <math>a_1=\frac{1}{2}, a_{-1}=\frac{1}{2}, a_k=0 \mbox{ for } k \ne 1,-1</math>
|-
| periodic square wave
<math>x(t)=\begin{cases} 
1,  & \mbox{if }t<T_1 \\
0, & \mbox{if }T_1<t<T/2 
\end{cases}</math> 

where T is the period and <math>2T_1</math> is the width of the pulse
| <math>\sum_{k=1}^N k^2 a_k e^{jk(\frac{2\pi}{T})t}</math>
(just the normal formula) 
| <math>a_k = \frac{2sin(k\omega_0T_1)}{k\omega_0T_1}</math>
|}

== Properties  of CT Fourier systems ==

{| border="1" class="wikitable"
|-
! Property 
! Periodic Signal 
! Fourier Series Coefficients
|-
|  
|  
| 
|-
| 
| 
| 
|}

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[[2011_Spring_ECE_301_Boutin|Back to ECE301 Spring 2011 Prof. Boutin]]