Difference between revisions of "Homework 4 ECE438F09" - Rhea

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

Latest revision as of 08:06, 20 September 2009