Problem 5 (3 pts) Prove the following transform relations (here û(w) = F{u(x)}): |x|

[answerhappygod]

Problem 5 3 Pts Prove The Following Transform Relations Here U W F U X X A X A A U X B U X 1 1 (85.64 KiB) Viewed 11 times

Problem 5 (3 pts) Prove the following transform relations (here û(w) = F{u(x)}): |x| <a |x| <a (a) u(x) (b) u(x) = = (1, lo, 1 x² + a²¹ (c) _u(x) = e-ax², a> 0 (a) F{x¹u(x)} = in û(n)(w) (b) F{eiaxu(x)} = û(w − a) (c) F{u(x − a)} = e-iaw û(w) a> 0 û(w) - û(w) û(w) = 2 sin aw ω = Пе Ξαω a TU 02 - e 4a a Problem 6 (3 pts) Derive the following basic properties of Fourier transform (here û(w) = F{u(x)}):