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Calculate the Fourier transforms of the following functions (you do not need to use any complex contour integration ): i) e-alæl, a > 0. (Hint: Use direct integration.) ii) e-ax? , a > 0. iii) cos(x)e-. (Hint: cos(x) = Re ei" .)

Calculate the Fourier transforms of the following functions (you do not need to use any complex contour integration ): i) e-alæl, a > 0. (Hint: Use direct integration.) ii) e-ax? , a > 0. iii) cos(x)e-. (Hint: cos(x) = Re ei" .)

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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Calculate the Fourier transforms of the following functions (you do not need to use any complex contour integration ): i) e-alel, a > 0. (Hint: Use direct integration.) ii) e-ax? , a > 0. iii) cos(x)e-a*. (Hint: cos(x) = Re et.) iv) cos(2x)/(4 + x²). (Hint: Apply the Fourier inversion theorem and i) above.)
Transcribed Image Text:Calculate the Fourier transforms of the following functions (you do not need to use any complex contour integration ): i) e-alel, a > 0. (Hint: Use direct integration.) ii) e-ax? , a > 0. iii) cos(x)e-a*. (Hint: cos(x) = Re et.) iv) cos(2x)/(4 + x²). (Hint: Apply the Fourier inversion theorem and i) above.)
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