bv_cvxbook_extra_exercises

Bv_cvxbook_extra_exercises

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Unformatted text preview: r quasiconvex optimization problem. (a) Maximum stopband attenuation. We fix ωc and N , and wish to maximize the stopband attenuation, i.e., minimize α. (b) Minimum transition band. We fix N and α, and want to minimize ωc , i.e., we set the stopband attenuation and filter length, and wish to minimize the ‘transition’ band (between π/3 and ωc ). (c) Shortest length filter. We fix ωc and α, and wish to find the smallest N that can meet the specifications, i.e., we seek the shortest length FIR filter that can meet the specifications. 93 (d) Numerical filter design. Use CVX to find the shortest length filter that satisfies the filter specifications with ωc = 0.4π, α = 0.0316. (The attenuation corresponds to −30dB.) For this subproblem, you may sample the constraints in frequency, which means the following. Choose K large (say, 500; an old rule of thumb is that K should be at least 15N ), and set ωk = kπ/K , k = 0, . . . , K . Then replace the specifications with • For k with 0 ≤ ωk ≤ π/3, 0.89 ≤ H (...
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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 University of California, Berkeley.

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