Announcements 2/22/12 Prayer Handouts, reading assignment for next lecture a. a.Dirac delta function b. b.Convolutions.

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Signals and Fourier Theory

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Presentation transcript:

Announcements 2/22/12 Prayer Handouts, reading assignment for next lecture a. a.Dirac delta function b. b.Convolutions

Reading Quiz The Fourier transform method we will be using most in this class involves: a. a.cosines b. b.sines c. c.complex exponentials

Reading Quiz Your book primarily uses which of the following notations to represent the Fourier transform of f(t)? a. a. f(  ) b. b. F {f(t)} c. c. FT{f(t)} d. d. g(t) e. 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. a.dissipation spectrum b. b.frequency spectrum c. c.Parseval spectrum d. d.power spectrum e. e.utility spectrum

Thought question (ungraded) What are the units of I(  )? a. a.intensity b. b.intensity/frequency c. c.intensity/frequency 2 d. d.intensity/time e. e.intensity/time 2 If you care, the actual units of intensity are W/m 2 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?