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<math>\delta(\omega)=\delta(2\pi f)=\frac{1}{2\pi}\delta(f)</math> |
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<math>\delta(\omega)=\delta(2\pi f)=\frac{1}{2\pi}\delta(f)</math> |
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{| border="0" cellpadding="0" cellspacing="0" |
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|<math>\int_{-\infty}^{\infty}\delta(a\,t)\,dt</math> |
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|<math>=\int_{-\infty}^{\infty}\delta(u\,t)\,\frac{du}{\left|a\right|}</math> |
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|Let <math>a\,t=u</math> and <math>du=a\,dt</math> |
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|<math>=\frac{1}{\left|a\right|}</math> |
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Revision as of 17:44, 17 November 2008
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Assuming the function is perodic with the period T
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Fourier Transform
Remember from 10/02 - Fourier Series
If we let
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Remember
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Definitions
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Examples
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Sifting property of the delta function
The dirac delta function is defined as any function, denoted as , that works for all variables that makes the following equation true:
- When dealing with , it behaves slightly different than dealing with . When dealing with , note that the delta function is . The is tacked onto the front. Thus, when dealing with , you will often need to multiply it by to cancel out the .
More properties of the delta function
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Let and
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