Prob. 3 (25 pt) If we express a directional spectrum over all frequency f and all direction in the following form: Elf,0

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Prob 3 25 Pt If We Express A Directional Spectrum Over All Frequency F And All Direction In The Following Form Elf 0 1 (38.49 KiB) Viewed 25 times

Prob. 3 (25 pt) If we express a directional spectrum over all frequency f and all direction in the following form: Elf,0) = E(H) H(fo) the directional spreading function H(f, o) can be displayed in a Fourier expansion with respect to wave direction) as TT H(f.°) = 1/2 + an() cos(nº) + bn(f) sin(no)] with n = 1, 2, 3, .. where the frequency dependent Fourier coefficient are and = SH(F. p)cos(no) do, and bu(h) = SH(f. )sin(no) do with the integration over all directions, 101 ST. Prove the following inequalities (ref: Lin et al. 1996) (a) lanch) bs (2)/2 (b) lanch) bil s 1/2 (c) (a (12 + [bn(f1s 1