bv_cvxbook_extra_exercises

# Bv_cvxbook_extra_exercises

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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 (...
View Full Document

## 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.

Ask a homework question - tutors are online