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| + | =Some General Purpose Formulas and Definitions= | ||
| − | = | + | {| |
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| + | ! colspan="2" style="background: #bbb; font-size: 110%;" | General Purpose Formulas | ||
| + | |- | ||
| + | ! colspan="2" style="background: #eee;" | Series | ||
| + | |- | ||
| + | | align="right" style="padding-right: 1em;" | [[Finite Geometric Series Formula_ECE301Fall2008mboutin]] || {{:Finite Geometric Series Formula_ECE301Fall2008mboutin}} | ||
| + | |- | ||
| + | | align="right" style="padding-right: 1em;" | [[Infinite Geometric Series Formula_ECE301Fall2008mboutin]] || {{:Infinite Geometric Series Formula_ECE301Fall2008mboutin}} | ||
| + | |- | ||
| + | ! colspan="2" style="background: #eee;" | Euler's Formula | ||
| + | |- | ||
| + | | 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;" | [[Cosine function in terms of complex exponential_ECE301Fall2008mboutin]] || {{:Cosine function in terms of complex exponential_ECE301Fall2008mboutin}} | ||
| + | |- | ||
| + | | align="right" style="padding-right: 1em;" | [[Sine function in terms of complex exponential_ECE301Fall2008mboutin]] || {{:Sine function in terms of complex exponential_ECE301Fall2008mboutin}} | ||
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| + | ! colspan="2" style="background: #eee;" | Definition of some Basic Functions (what engineers call "Signals") | ||
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| + | | align="right" style="padding-right: 1em;" | [[sinc function_ECE301Fall2008mboutin]] || {{:sinc function_ECE301Fall2008mboutin}} | ||
| + | |- | ||
| + | |} | ||
| − | + | ----- | |
| − | + | [[ MegaCollectiveTableTrial1|Back to Collective Table]] | |
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| − | [[ MegaCollectiveTableTrial1|Back to | + | |
Revision as of 04:47, 27 October 2009
Some General Purpose Formulas and Definitions
| General Purpose Formulas | |
|---|---|
| Series | |
| Finite Geometric Series Formula_ECE301Fall2008mboutin | $ \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_ECE301Fall2008mboutin | $ \sum_{k=0}^\infty 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 | |
| Complex exponential in terms of sinusoidal signals_ECE301Fall2008mboutin | $ 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} $ |
