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[[ECE438_(BoutinFall2009)|Back to ECE438 course page]]
 
  
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==Scaling of the Dirac Delta (Impulse Function)==
 
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<math>\displaystyle\delta(\alpha f)=\frac{1}{\alpha}\delta(f)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;for\;\;\alpha>0</math>
 
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==Mini Proof==
 
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<math>\int_{-\infty}^{\infty}\delta(x)dx = 1</math>
 
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<math>\displaystyle Let\;\;\;y=\alpha x\;\;\;\;\;\;\;\;\;\;\;\;\;dx=\frac{dy}{\alpha}</math>               
 
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<math>\displaystyle\int_{-\infty}^{\infty}\delta(\alpha x)dx=\int_{-\infty}^{\infty}\delta(y)\frac{dy}{\alpha}=\frac{1}{\alpha}</math>
 
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==Hence,==
 
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<math>\displaystyle\delta(\omega)=\delta(2\pi f)=\frac{1}{2\pi}\delta(f)</math>
 

Latest revision as of 08:06, 20 September 2009

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Basic linear algebra uncovers and clarifies very important geometry and algebra.

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