Optimal design of FIR filter with discrete coefficients based on integer semi-infinite linear programs

Optimal design of IIR filters using linear semi‐indefinite programming method

“…In this phase, active constraint candidates are selected for problem (11). For this purpose, ω is discretized into S elements on Ω, r is discretized into T elements on Φ, and ω′ is discretized into U elements on Ω′; thus, problem (11) is reduced to the following problem with a finite number of constraints:…”

“…Let us assume that L pairs of ω l , r l and P values of ω m g were obtained in the integration phase. These are approximate solutions to problem (11), and are assumed to be close to the true active constraint ω, r, ω'. In the adjustment phase,…”

“…, and x are treated as initial values, and the active constraints are adjusted so as to meet the Karush-Kuhn-Tucker conditions [12], which are optimality conditions for solution to problem (11). Here x is the solution to Eq.…”

“…In this study, we propose a new method for design problems formulated by means of the real rotation theorem; in particular, we combine the three-phase method [11] (an algorithm for LSIP solving) with the iterative simplex method. The simplex method is employed for the derivation of approximate solutions that are required in order to find optimal solutions to the LSIP, and as a result, the solved problem can be reduced to a relatively small scale.…”