Riitta Niemistö

Multistage IIR filter design using convex stability domains defined by positive realness

In this paper, we consider infinite impulse response (IIR) filter design where both magnitude and phase are optimized using a weighted and sampled least-squares criterion. We propose a new convex stability domain defined by positive realness for ensuring the stability of the filter and adapt the Steiglitz-McBride (SM), Gauss-Newton (GN), and classical descent methods to the new stability domain. We show how to describe the stability domain such that the description is suited to semidefinite programming and is implementable exactly; in addition, we prove that this domain contains the domain given by Rouche/spl acute/s theorem. Finally, we give experimental evidence that the best designs are usually obtained with a multistage algorithm, where the three above methods are used in succession, each one being initialized with the result of the previous and where the positive realness stability domain is used instead of that defined by Rouche/spl acute/s theorem.

Simplified procedures for quasi-equiripple IIR filter design

Simplified procedures for quasi-equiripple infinite-impulse response (IIR) filter design are proposed. The procedures can be applied in designs where the number of poles is low compared to the number of zeros. The design is initialized with an IIR filter optimizing a least squares criterion. In the simplified procedures, namely simplified iterative reweighting and fixed poles least pth design, the poles of the filter are kept fixed in the succeeding iterative optimization of the numerator. The simplified designs are compared to complete iterative reweighting, where complete IIR design is performed at each iteration. The simplified design is much faster with very small departure from optimality.

SDP design procedure for energy compaction IIR filters

We present a design method for optimal energy compaction IIR filters, where the numerator and denominator may have different degrees. The design is performed via iterative relaxations, where the numerator is optimized given the denominator, followed by optimization of denominator given the numerator. The two optimization problems involved are solved using semidefinite programming (SDP) techniques, where the real positiveness of the causal part of the product filter is formulated in two alternative ways: first using the Kalman-Yakubovich-Popov (KYP) lemma, and second, by a less-known parameterization (Genin et al., 2000; Stoica et al., 2000), which we show to be more convenient numerically. Numerical results show the effectiveness of the proposed method and the improvements when compared with optimal FIR compaction filters or constrained IIR compaction filters (restricted to have allpass polyphase components).

SDP design procedures for near-optimum IIR compaction filters

In this paper we present two new design methods for IIR compaction filters, where the numerator and denominator may have different degrees. In the first method, the design is performed via iterative relaxations, where the numerator is optimized given the denominator, followed by optimization of denominator given the numerator. The second method sets the poles at fixed angles given by the ideal brickwall filter and optimizes the numerator. Both methods rely on semidefinite programming optimization, using an appropriate parameterization of positive real polynomials. Experimental results show compaction gains near the upper bound given by the ideal filter. The IIR filters may be implemented with significantly less parameters than the FIR counterparts achieving the same compaction gain.

Optimization of IIR compaction filters with fixed angles poles

We present a new design method for IIR compaction filters, where the numerator and denominator may have different degrees. The method sets the poles at fixed angles given by the ideal brickwall filter and optimizes the numerator. The method relies on semidefinite programming optimization, using an appropriate parameterization of positive real polynomials. Experimental results show compaction gains near the upper bound given by the ideal filter. The IIR filter may be implemented with significantly less parameters than the FIR counterparts that achieve the same compaction gain.

A fast algorithms for adaptive polynomial filtering

This paper introduces a fast adaptive polynomial filtering algorithm, called LS-LMS algorithm, and analyzes its connections with RLS and with several QR decomposition based adaptive algorithms introduced in (Liu, 1995) and (Niemisto et al., 1996). Since the time-shift invariance property of the input data (Haykin, 1996, p. 763) is not required for the input vector, the algorithm is well suited for the identification of polynomial models. A noise cancelation application exemplifies the benefits of using the new algorithm.