bv_cvxbook_extra_exercises

# Hint you can generate samples of the price change

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Unformatted text preview: ﬃcients hkl above are not exactly the same as the impulse response coeﬃcients of the ﬁlter.) We will design a 2D ﬁlter (i.e., ﬁnd the coeﬃcients hkl ) to satisfy H (0, 0) = 1 and to minimize the maximum response R in the rejection region Ωrej ⊂ [0, π ]2 , R= sup (ω1 ,ω2 )∈Ωrej | H ( ω1 , ω2 ) | . (a) Explain why this 2D ﬁlter design problem is convex. (b) Find the optimal ﬁlter for the speciﬁc case with N = 5 and 2 2 Ωrej = {(ω1 , ω2 ) ∈ [0, π ]2 | ω1 + ω2 ≥ W 2 }, with W = π/4. You can approximate R by sampling on a grid of frequency values. Deﬁne ω (p) = π (p − 1)/M, p = 1, . . . , M. (You can use M = 25.) We then replace the exact expression for R above with ˆ R = max{|H (ω (p) , ω (q) )| | p, q = 1, . . . , M, (ω (p) , ω (q) ) ∈ Ωrej }. ˆ Give the optimal value of R. Plot the optimal frequency response using plot_2D_filt(h), available on the course web site, where h is the matrix containing the coeﬃcients hkl . 100 12.11 Maximizing log ut...
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## This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at Berkeley.

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