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