Odd-Order Variable-Bandwidth Digital Filter Using Lp-Norm-Error Minimization

This paper details a 2-step tactic for implementing an odd-order (OO) variable-bandwidth (VBW) filter with absolutely guaranteed stability. The design scheme minimizes the Lp-norm of weighted amplitude-response-error vector, and the OO-VBW filter coefficients are formed using polynomials in the bandwidth (BW)-varying parameter. Since those coefficients have variable function values, the designed OO-VBW filter possesses variable amplitude response. Another crucial issue discussed in this paper is about stability guarantee. Since changing the filter coefficients (in terms of the polynomial-function values) may cause instability, the stability must be ensured during online tuning. A coefficient-conversion (CC) technique is employed for achieving this objective. A bandpass OO-VBW filter is simulated for validating the presented 2-step tactic as well the stability guarantee.