s21_ps14_sol

# s21_ps14_sol - Uniﬁed Engineering II Spring 2004 Problem...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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 S21 (Signals and Systems) Solution: 1. The signal is plotted below: 1.2 1 g(t) 0.8 0.6 0.4 0.2 0 -10 -8 -6 -4 -2 0 Time, t 2 4 6 8 10 The signal is very smooth, almost like a Gaussian. Therefore, I expect that the duration bandwidth product will be close to the theoretical lower bound. 2. � Δt 2 �2 � 22 t g (t) dt =�2 g (t) dt The two integrals are easily evaluated for the given g (t). The result is � 7 t2 g 2 (t) dt = 2 � 5 g 2 (t) dt = 2 Therefore, � 7 Δt = 2 5 3. The time domain formula for the bandwidth is � �2 � 2 g (t) dt ˙ Δω =� 2 2 g (t) dt The numerator integral is � g 2 (t) dt = ˙ 1 2 Therefore, 2 Δω = √ 5 4. The duration­bandwidth product is √ 47 Δt Δω = ≈ 2.1166 5 which is very close to the theoretical lower limit of 2. This is not surprising, since the shape of g (t) is close to a gaussian. ...
View Full Document

## This note was uploaded on 01/28/2012 for the course AERO 16.01 taught by Professor Markdrela during the Fall '05 term at MIT.

### Page1 / 2

s21_ps14_sol - Uniﬁed Engineering II Spring 2004 Problem...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online