Summary

• Adding two waves of different ω
• Adding waves of different v
• Intro to Fourier Series

• Fourier series
• Fourier series applet
• Periodic functions
• Nonperiodic functions
• in-class 7.38
• the sinc(x) function

Hecht4 7.38
Write an expression for the transform A(ω) of the harmonic pulse of Fig. P.7.38. Check that sinc(u) is 50% or greater for values of u roughly less than π/2. With that in mind, show that ΔfΔt ≈ 1, where Δf is the bandwidth of the transform at half its maximum amplitude. Verify that ΔfΔt ≈ 1 at half the maximum value of the power spectrum as well. The purpose here is to get some sense of the kind of approximations used in the discussion.