Prove that the Dirac delta function satisfies +∞ 1 S(t – t') = 2/= t 2π ģ exp(-iw[t − t']) dw,
Prove that the Dirac delta function satisfies +∞ 1 S(t – t') = 2/= t 2π ģ exp(-iw[t − t']) dw,
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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How can I prove this? I know that it works by applying Fourier Inverse Theorem but I don't really know how.
![Prove that the Dirac delta function satisfies
•+∞
8( t - t') 12/7000 exp(-iwt- t']) dw,
=
2πT
∞](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2521d3ac-1f2b-4213-a1c7-670c7b844752%2Faecf9030-b99c-4cda-a4da-f03db6297ff1%2F8jjrg5f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Prove that the Dirac delta function satisfies
•+∞
8( t - t') 12/7000 exp(-iwt- t']) dw,
=
2πT
∞
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