Latest revision as of 07:23, 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	$E_\infty=\sum_{n=-\infty}^\infty \| x[n] \|^2$

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@@ Line 6: / Line 6: @@
 ! 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 exponential_ECE301Fall2008mboutin]] || {{:Sine function in terms of complex exponential_ECE301Fall2008mboutin}}
-|-
-! 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}}
 |-
 |}

Difference between revisions of "SomeGeneralPurposeFormulas1" - Rhea

Latest revision as of 07:23, 29 October 2009

Some General Purpose Formulas and Definitions

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