A Fourier transform is another integral transform often used in higher mathematics. The Fourier transform of f(t), denoted as F(w), is defined as F(w) = = f(t)e-hot dt where w is a real number and i is the imaginary unit (= √−1). Let a > 0. Find the Fourier transform of f(at). Your answer must include F, w, and a (among other symbols), but no integrals.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question
A Fourier transform is another integral transform often used in higher
mathematics. The Fourier transform of f(t), denoted as F(w), is defined as
F(w) = f(t)e-tout dt
where w is a real number and i is the imaginary unit (= √-1).
Let a > 0. Find the Fourier transform of f(at). Your answer must include F, w, and a
(among other symbols), but no integrals.
Transcribed Image Text:A Fourier transform is another integral transform often used in higher mathematics. The Fourier transform of f(t), denoted as F(w), is defined as F(w) = f(t)e-tout dt where w is a real number and i is the imaginary unit (= √-1). Let a > 0. Find the Fourier transform of f(at). Your answer must include F, w, and a (among other symbols), but no integrals.
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