Problem 26 of 36 prove parsevals theorem let f be

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 0 (1−iω)x e −∞ e−(1+iω)x dx = −(1 + iω) 2 = 1 + ω2 ∞ 0 e−(1−iω)x + −(1 − iω) ∞ 0 3. (Problem 26 of 3.6) Prove Parseval’s theorem. Let f be real-valued, continuous and piecewise ∞ ∞ |f (x)|dx and smooth on the real line. Assume that −∞ Then ∞ 1 f (x)dx = 2π −∞ 2 Answer 1 −∞ ∞ −∞ |f (ω)|2 dω. f 2 (x)dx converge. First, note that the complex conjugate of f is ∞ ∗ (f ) (ω ) = ∗ −iωx fe dx ∞ ∗ iωx = −∞ fe ∞ f eiωx dx dx = −∞ ...
View Full Document

This document was uploaded on 03/02/2014 for the course MATH Math4052 at HKUST.

Ask a homework question - tutors are online