Write an expression for the transform A( Iuml ) of the harmonic pulse of Fig P 7 54 Check that sinc u is 50 or greater for values of u roughly less than Iuml 2 With that in mind, show that Icirc v Icirc t 1, where Icirc v is the bandwidth of the transform at half its maximum amplitude Verify that I...

By analogy with Eq 761 sinc p t2 From Table ...

Write an expression for the transform A(Ï) of the harmonic pulse of Fig. P.7.54. Check that sinc

Question:

Write an expression for the transform A(Ï‰) 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 Î”v Î”t ‰ˆ 1, where Î”v is the bandwidth of the transform at half its maximum amplitude. Verify that Î”v Î”t ‰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 Δt.