Derivations NIP course
نویسنده
چکیده
Q: Consider an uncorrelated (white) Gaussian signal s(t). Calculate its 3rd and 4th order moments, m3 = ⟨s(t1)s(t2)s(t3)⟩ and m4 = ⟨s(t1)s(t2)s(t3)s(t4)⟩. Confirm with simulation. The third moment m3 = ⟨s(t1)s(t2)s(t3)⟩ is zero. Namely, if t1 ̸= t2 ̸= t3 then m3 = ⟨s⟩ = 03 = 0. If t1 = t2 = t3, m3 = ⟨ s3 ⟩ = ́ N (0, σ2)x3dx = 0, as this is the integral over an odd function. For t1 = t2 ̸= t3, m3 = ⟨s⟩ ⟨ s2 ⟩ = 0.σ2 = 0. Consider m4 = ⟨s(t1)s(t2)s(t3)s(t4)⟩. Here we have contributions when t1 = t2 and t3 = t4 and permutation
منابع مشابه
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