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Validate the inverse Fourier transform undoes the Fourier transform by substitution f(x) = √/12/17 100 g(k)eikx dk = F¯¹[g(k)] √√2TT -∞ g (k) = √/12/17 f(x) e dx = F[f(x)] -ikx -0

Validate the inverse Fourier transform undoes the Fourier transform by substitution f(x) = √/12/17 100 g(k)eikx dk = F¯¹[g(k)] √√2TT -∞ g (k) = √/12/17 f(x) e dx = F[f(x)] -ikx -0

Advanced Engineering Mathematics
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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Validate the inverse Fourier transform undoes the Fourier transform by substitution ∞ 1 f(x) √²/₁9 (k) e¹kx dk = F-¹ [g(k)] -∞ ∞ -ikx g (k)=√ √/12/17 f(x) e dx = F[f(x)] 2π -X
Transcribed Image Text:Validate the inverse Fourier transform undoes the Fourier transform by substitution ∞ 1 f(x) √²/₁9 (k) e¹kx dk = F-¹ [g(k)] -∞ ∞ -ikx g (k)=√ √/12/17 f(x) e dx = F[f(x)] 2π -X
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