Write an expression for the transform A(ω) of the harmonic pulse of Fig. P.7.54. Check that sinc u is 50% or greater for values of u roughly less than Ï€/2. With that in mind, show that Δv Δt ‰ˆ 1, where Δv is the bandwidth of the transform at half its maximum amplitude. Verify that Δv Δt ‰ˆ 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.

Figure P.7.54 E(t) E, E(t) = E, cos w, t t.