Announcements 2/22/12


Prayer
Handouts, reading assignment for next lecture
a. Dirac delta function
b. Convolutions
Reading Quiz

The Fourier transform method we will be using
most in this class involves:
a. cosines
b. sines
c. complex exponentials
Reading Quiz

Your book primarily uses which of the
following notations to represent the Fourier
transform of f(t)?
a. f(w)
b.
F {f(t)}
c. FT{f(t)}
d. g(t)
e. g(w)
Fourier transform of Gaussian wavepacket
T = 1.5, w0 = 10
Fourier transform of Gaussian wavepacket, cont.
T = 1.5, w0 = 10
(original)
T = 3.5, w0 = 10
(longer duration)
Fourier transform of Gaussian wavepacket, cont.
= 1.5, w0 = 10
(original)
= 0.35, w0 = 10
(shorter duration)
How to get single peaks in F.T.
Uncertainty Principle
Reading Quiz

We learned that the time-averaged intensity
n 0 c
2
I
(
r
,
t
)

E
(
r
,
t
)
relates to the electric field as
.
2
What is this other, closely-related, quantity
called? I (r, w )  n 0c E (r, w ) 2
2
a.
b.
c.
d.
e.
dissipation spectrum
frequency spectrum
Parseval spectrum
power spectrum
utility spectrum
Thought question (ungraded)

What are the units of I(w)?
a. intensity
b. intensity/frequency
c. intensity/frequency2
d. intensity/time
e. 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, w0 = 10 (original)
|E(t)|2
|E(w)|2
Are the areas equal?