FIR–IIR adaptive filters hybrid combination

Abstract

To enhance the performance in IIR system identification scenarios, a hybrid combination of FIR and IIR adaptive filters (AFs) via a supervisor that senses which one is performing best is proposed. The FIR-LMS AF is short, providing fast and robust convergence, whereas the IIR-LMS AF is slow but accurate. The stagnation effect caused by the different convergence rates is tackled through cyclic weight transfers FIR → IIR, which also ensure good tracking properties. A design technique for the transfers cycle length is proposed, providing good convergence while keeping computational cost low.

VLSI Design of a High Performance Decimation Filter Used for Digital Filtering

“…The digital filter is described by difference equation in time domain and by transfer function in frequency domain [6]. There are two basic types of digital filters: Finite impulse response (FIR) filters and infinite impulse response (IIR) filters [7]. The both types of filters have some advantages and disadvantages are summarized in Table I.…”

Hybrid convex combinations for IIR system identification.

“…We suggested in [28] inherently more dicult to analyze than their FIR counterparts, the energy conservation principles proved to t well into the IIR adaptive ltering framework.…”

“…Section 4.2 shows a FIR-IIR AFs combination (the T-OE) for the system identication setup that we rst introduced in [28], which shows improved performance over an ordinary IIR AF while keeping the computational complexity low by skipping 5 This is a well known issue in linear algebra: the solution of ill-conditioned systems is extremely sensitive to small perturbations and no numerical trick can prevent that [27]. In case of stochastic gradient-based algorithms, the adaptation itself is disturbing due the gradient noise; so, the optimal solution will take longer to be achieved, regardless of the algorithm used.…”

“…As such, the supervisor compares the relative performance of both components by checking the mixing factor λ(i) every L iterations and enable the transfers only when necessary. Succinctly, the T-OE is described in Algorithm 1 [28].…”

Combinations of adaptive filters.

“…Other solutions have been proposed, such as data reusing (DR) [22][23][24][25], mixed-norm updates [26][27][28][29], and variable step size (VSS) [30][31][32]. Combinations of AFs, however, have shown several advantages over these techniques in terms of performance and robustness [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49]. In some cases, it even provides a more general framework under which these adaptive algorithms can be cast (as argued in Chapter 8).…”