Revision as of 05:51, 27 October 2009

Some General Purpose Formulas and Definitions

General Purpose Formulas
Series
Finite Geometric Series Formula	$\sum_{k=0}^n x^k = \left\{ \begin{array}{ll} \frac{1-x^{n+1}}{1-x}&, \text{ if } x\neq 1\\ n+1 &, \text{ else}\end{array}\right.$
Infinite Geometric Series Formula	$\sum_{k=0}^n x^k = \left\{ \begin{array}{ll} \frac{1}{1-x}&, \text{ if } \|x\|\leq 1\\ \text{diverges} &, \text{ else }\end{array}\right.$
Euler's Formula and Related Equalities
Euler's formula	$e^{jw_0t}=cosw_0t+jsinw_0t$
Cosine function in terms of complex exponential_ECE301Fall2008mboutin	$cos\theta=\frac{e^{j\theta}+e^{-j\theta}}{2}$
Sine function in terms of complex exponential_ECE301Fall2008mboutin	$sin\theta=\frac{e^{j\theta}-e^{-j\theta}}{2j}$
Definition of some Basic Functions (what engineers call "Signals")
sinc function_ECE301Fall2008mboutin	$sinc(\theta)=\frac{sin(\pi\theta)}{\pi\theta}$

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-! colspan="2" style="background: #eee;" | Euler's Formula and related equalities
+! colspan="2" style="background: #eee;" | Euler's Formula and Related Equalities
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-| align="right" style="padding-right: 1em;" | [[Complex exponential in terms of sinusoidal signals_ECE301Fall2008mboutin]] || {{:Complex exponential in terms of sinusoidal signals_ECE301Fall2008mboutin}}
+| align="right" style="padding-right: 1em;" | Euler's formula || <math>e^{jw_0t}=cosw_0t+jsinw_0t</math>
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 | align="right" style="padding-right: 1em;" | [[Cosine function in terms of complex exponential_ECE301Fall2008mboutin]] || {{:Cosine function in terms of complex exponential_ECE301Fall2008mboutin}}