Frequency-domain adaptive filtering using continuous transfer functions

A continuous-time frequency-domain adaptive filtering approach is described. The adaptive filter is required to allow independent control of its transfer function coefficients. A sequential-linear-search (SLS) adaptation algorithm is presented and its convergence properties are investigated. It is shown analytically that the algorithm converges to a global solution with respect to the numerator coefficients of any adaptive transfer function order. The error surface as a function of the denominator coefficients is studied numerically for orders up to the third. Practical considerations for implementation purposes are presented. The filter configuration suggested is shown to be MOS integrable using switched capacitor techniques. The proposed algorithm was applied successfully to adapt to rational and irrational unknown systems using second and third order adaptive filters.