s22_ps14_sol

s22_ps14_sol - Unified Engineering II Spring 2004 Problem...

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: Unified Engineering II Spring 2004 Problem S22 (Signals and Systems) Solution: I used Mathematica to find some of the integrals, although you could use tables or integrate by parts. (a) ¯ t= � ∞ � 2 t7 e−2t/tau dt = 315 8 τ 16 t6 e−2t/tau dt = tg (t) dt = 45 7 τ 8 0 ¯ t= � � 2 ∞ g (t) dt = 0 Therefore, ¯7 t= τ 2 (b) � ¯ (t − t)2 g 2 (t) dt = Therefore, Δt = √ 315 9 τ 32 7 τ (c) � 9 g 2 (t) dt = τ 5 ˙ 8 Therefore, 2 Δω = √ 5τ (d) The duration­bandwidth product is � Δt Δω = 2 7 ≈ 2.366 5 which compares favotably with the theoretical lower bound Δt Δω ≥ 2 ...
View Full Document

Ask a homework question - tutors are online