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(ELEC317)midtermQ3sol.pdf
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3 (a) A-1=AH
(b) Energy of U = tr(UHU)
Energy of V = tr(VHV)
=tr((AU) H (AU))
=tr(UH AH AU)
=tr(UH I U)
=tr(UH U)
(c) v*(N-k) = Cu*(n)W(N-k)n* where C=1/N
= Cu(n) W-Nn+kn since u(n)=u*(n)
= Cu(n)Wkn since W-Nn=exp(-j2npi)=1
= v(k)