Max Gerken

A hybrid least squares QR-lattice algorithm using a priori errors

This paper presents a new minimal and backward stable QR-LSL algorithm obtained through the proper interpretation of the system matrix that describes the adaptation and filtering operations of QR-RLS algorithms. The new algorithm is based on a priori prediction errors normalized by the a posteriori prediction error energy-as suggested by the interpretation of the system matrix-and uses the fact that the latter quantities can be computed via a lattice structure. Backward consistency and backward stability become guaranteed under simple numerical conventions. In contrast with the known a posteriori QR-LSL algorithm, the new algorithm present; fewer numerical complexity, and backward consistency is guaranteed without the constraint of passive rotations in the recursive lattice section. Furthermore, reordering of some operations results in a version with identical numerical behavior and inherent parallelism that can be exploited for fast implementations. Both a priori and a posteriori QR-LSL algorithms are compared by means of simulations. For small mantissa wordlengths and forgetting factors /spl lambda/ not too close to 1, the proposed algorithm performs better due to dispensing with passive rotations. For forgetting factors very close to one and small wordlengths, both algorithms are sensitive to the accuracy of some well-identified computations.

Joint position and amplitude search of algebraic multipulses

A joint position and amplitude search algorithm is proposed for algebraic multipulse codebooks to be used in code-excited linear predictive (CELP) coders. The joint search complexity is below one quarter that of the focused search and ranks below those of the G.729A and IS-641-A coders. Listening tests indicate an equivalence in perceived quality.

A hybrid QR-lattice least squares algorithm using a priori errors

A fast algorithm for RLS filtering is presented which is a hybrid between QR and lattice algorithms. Its prediction section is based upon normalized a priori prediction errors. It is of minimal complexity and, using simple numerical conventions, is backward stable under persistent excitation.

A polyphase IIR adaptive filter: error surface analysis and application

An analysis of the local convergence speed of constant gain algorithms for direct form IIR adaptive filters is initially presented, showing the adverse effects that result from the proximity of the poles of the modelled system to the unit circle and, for complex poles, to the real axis. A global analysis of the reduced error surface in these cases is also presented, which shows that, away from the global minimum, there will be regions with an almost constant error, where the convergence of constant gain algorithms tends to be slow. A polyphase IIR adaptive filter is then proposed and its local and global convergence properties are investigated, showing it to be specially well suited for applications with underdamped low-frequency poles. The polyphase structure is tested with different constant gain algorithms in an echo-cancellation example, attaining a gain of 14 to 70 times in global convergence speed over the direct form, at the price of a relatively modest increase in computational complexity. A theorem concerning the existence of stationary points for the polyphase structure is also presented.

A multistage search of algebraic CELP codebooks

A joint amplitude and position search procedure is proposed for searching algebraic multipulse codebooks. It is implemented within the reference G.723.1 codec as an example. This joint search method is shown to reduce down to one third the number of comparisons per subframe relative to the focused search over an extensive speech database. An efficient implementation of the joint search is derived which incorporates backward filtering of the residual target vector and precomputation of autocorrelation elements, bringing about a reduction in complexity of one-third in comparison to the focused search. The joint search performs about one thirtieth as many comparisons as the full position search.

A stable and efficient DSP implementation of a LSL algorithm for acoustic echo cancelling

We present an optimized DSP implementation of a modified error-feedback lattice least-square (EF-LSL) adaptive filtering algorithm. Simple measures that provide numerical stability for poor persistent excitation are also proposed. As a result of the optimization and the stability measures, an efficient and stable implementation of a fast algorithm of the RLS family was attained. We present the results of an acoustic echo cancelling experiment performed with the implemented algorithm. With a 40 MIPS SHARC DSP, up to 290 adaptive filter coefficients can be used. This represents an effective alternative to algorithms of the LMS family, while still retaining the good convergence properties of the RLS family.

Allpass transfer functions with prescribed group delay

This paper presents a method for the design of discrete-time allpass transfer functions with prescribed group delay. The design procedure consists in computing the unit pulse response of an associated stable and minimal phase system using coefficients from the Fourier series expansion of the specified group delay. The allpass coefficients are computed from the unit pulse response using Pronys method. The procedure allows the design of allpass functions with prescribed number of stable and unstable poles. It is useful as an approximation method by itself but the major motivation for developing it was to systematically obtain initial solutions for the design of digital filters consisting of the parallel connection of two allpass filters.<<ETX>>

Performance of the a priori and a posteriori QR-LSL algorithms in a limited precision environment

The performance of two minimal QR-LSL algorithms in a low precision environment is investigated. For both algorithms backward consistency and backward stability become guaranteed under simple numerical conventions. They present stable behaviour even when excited with ill conditioned signals such as predictable signals. Since the problem of ensuring numerical stability is solved for these algorithms, an investigation about their accuracy is in place. By simulating a channel equalizer configuration it is shown that, for small mantissa wordlengths and forgetting factors /spl lambda/ not too close to 1, the a priori algorithm performs better due to its dispensing with passive rotations. For forgetting factors very close to one and small wordlengths, both algorithms are sensitive to the accuracy of some well-identified computations. They are compared to an LSL algorithm, based on a priori prediction errors, whose good performance in limited precision environments is known.

A polyphase IIR adaptive filter

A polyphase structure for infinite-impulse response (IIR) adaptive filtering is proposed and compared to the direct structure in terms of their reduced error surface. It is shown that the general shape of its surface can make the polyphase structure have higher convergence speed, alleviating the problem of convergence speed in IIR adaptive filters and allowing their computational complexity gain over finite-impulse response (FIR) adaptive filters to be exploited. Benefits regarding filter stability are also achieved with the polyphase structure. An example of a high-speed digital subscriber line (HDSL) application is presented, for which the polyphase structure attains a gain of up to 70 times in convergence speed over an IIR direct structure, leading to roughly the same convergence speed of a FIR structure but with only 12% of its computational complexity. The question of uniqueness of the stationary points of the proposed structure is also discussed. It is pointed out that for white input and sufficient modeling, all stationary points are global minima, a result which does not follow directly from an equivalent property of the direct structure.

An adaptive filtering algorithm with parameter acceleration

We introduce a novel fast discrete-time algorithm for adaptive filtering applications. It is based on a tuner used in adaptive control that sets the second derivative of the parameter estimates. For colored input signals the proposed algorithm presents a more favorable compromise between convergence speed and steady-state estimation error than the LMS or NLMS algorithms, a property obtained at the cost of a moderate increase in computational complexity. We provide a deterministic convergence proof and present simulation results.