(5 intermediate revisions by the same user not shown)
Line 6: Line 6:
 
! colspan="2" style="background: #bbb; font-size: 110%;" | General Purpose Formulas
 
! colspan="2" style="background: #bbb; font-size: 110%;" | General Purpose Formulas
 
|-
 
|-
−
! colspan="2" style="background: #eee;" | Series
+
! colspan="2" style="background: #eee;" | Function (or Signal) Metrics
 
|-
 
|-
−
| align="right" style="padding-right: 1em;" | Finite Geometric Series Formula || <math>\sum_{k=0}^n x^k = \left\{ \begin{array}{ll} \frac{1-x^{n+1}}{1-x}&, \text{ if } x\neq 1\\ n+1 &,  \text{ else}\end{array}\right. </math>
+
| align="right" style="padding-right: 1em;" | CT signal energy || <math>E_\infty=\int_{-\infty}^\infty | x(t) |^2 dt </math>
−
 
+
|-  
−
|-
+
| align="right" style="padding-right: 1em;" | DT signal energy || <math>E_\infty=\sum_{n=-\infty}^\infty | x[n] |^2 </math>
−
| align="right" style="padding-right: 1em;" | Infinite Geometric Series Formula || <math>\sum_{k=0}^n x^k = \left\{ \begin{array}{ll} \frac{1}{1-x}&, \text{ if } |x|\leq 1\\ \text{diverges} &, \text{ else }\end{array}\right. </math>
+
−
 
+
−
|-
+
−
! colspan="2" style="background: #eee;" | Euler's Formula and Related Equalities
+
−
|-
+
−
| align="right" style="padding-right: 1em;" | Euler's formula || <math>e^{jw_0t}=cosw_0t+jsinw_0t</math>
+
−
|-
+
−
| align="right" style="padding-right: 1em;" | Cosine function in terms of complex exponentials|| <math>cos\theta=\frac{e^{j\theta}+e^{-j\theta}}{2}</math>
+
−
|-
+
−
| align="right" style="padding-right: 1em;" | Sine function in terms of complex exponentials||<math>sin\theta=\frac{e^{j\theta}-e^{-j\theta}}{2j}</math>
+
−
 
+
−
|-
+
−
! colspan="2" style="background: #eee;" | Definition of some Basic Functions (what engineers call "Signals")
+
−
|-
+
−
| align="right" style="padding-right: 1em;" | [[sinc function_ECE301Fall2008mboutin]] || {{:sinc function_ECE301Fall2008mboutin}}
+
 
|-  
 
|-  
 
|}
 
|}

Latest revision as of 06:23, 29 October 2009

Some General Purpose Formulas and Definitions

General Purpose Formulas
Function (or Signal) Metrics
CT signal energy $ E_\infty=\int_{-\infty}^\infty | x(t) |^2 dt $
DT signal energy $ E_\infty=\sum_{n=-\infty}^\infty | x[n] |^2 $

Back to Collective Table

Retrieved from "https://www.projectrhea.org/rhea/index.php?title=SomeGeneralPurposeFormulas1&oldid=36065"
Shortcuts
Help Main Wiki Page Random Page Special Pages Log in
Search

Alumni Liaison

Meet a recent graduate heading to Sweden for a Postdoctorate.

Christine Berkesch