Design of Linear-Phase FIR Filters with Time and Frequency Domains Constraints by Means of AI Based Method

We consider a constrained finite-impulse response (FIR) filter design with time-and frequency-domain piece-wise linear constraints. This type of constrained FIR filter design usually employs the least-squares error criterion and can be generally reformulated as quadratic programming (QP) problem. This paper presents a new algorithm for the design of constrained low-pass FIR filters describing the design problem in terms of the epsilon-insensitive learning derived from AI methods. This approach is based on a dedicated new method for solution of an over-determined system of linear equations. This method tolerates very well the increase of the number of filter coefficients and/or the number of constraints. The proposed method is also characterized by rapid convergence and is suitable for high order filter design.