Announcements 2/22/12 Prayer Handouts, reading assignment for next

lecturea. Dirac delta functionb. Convolutions

Reading Quiz The Fourier transform method we will be

using most in this class involves:a. cosinesb. sinesc. complex exponentials

Reading Quiz Your book primarily uses which of the

following notations to represent the Fourier transform of f(t)?

a. f()b. F {f(t)}c. FT{f(t)}d. g(t)e. g()

Fourier transform of Gaussian wavepacket

T = 1.5, 0 = 10

Fourier transform of Gaussian wavepacket, cont.

T = 1.5, 0 = 10(original)

T = 3.5, 0 = 10(longer duration)

Fourier transform of Gaussian wavepacket, cont.

= 1.5, 0 = 10(original)

= 0.35, 0 = 10(shorter duration)

How to get single peaks in F.T.

Uncertainty Principle

Reading Quiz We learned that the time-averaged

intensity relates to the electric field as . What is this other, closely-related, quantity called?

a. dissipation spectrumb. frequency spectrum c. Parseval spectrumd. power spectrume. utility spectrum

20( , ) ( , )2n cI t E t

r r

20( , ) ( , )2n c

I E

r r

Thought question (ungraded) What are the units of I()?

a. intensityb. intensity/frequencyc. intensity/frequency2

d. intensity/timee. intensity/time2

If you care, the actual units of intensity are W/m2 and the units of frequency are s-1 (or more

technically rad/s). But you should be able to figure this question out without knowing any of that.

Parseval’s Theorem Example= 1.5, 0 = 10 (original)

|E(t)|2

|E()|2

Are the areas equal?