Multi-step optimal quantization in oversampled filter banks

Using concepts from the receding horizon control framework, we propose an approach to quantization in oversampled filter banks. The key idea is to pose the quantization problem as a multi-step optimization problem, where the decision variables are restricted to belong to a finite set. It is shown that the resulting architecture yields enhanced performance when compared to the well-known noise shaping coder. In particular, the quantizer proposed can be tuned with stability concepts in mind.

[1]  Graham C. Goodwin,et al.  Multi-Step Optimal Analog-to-Digital Conversion , 2022 .

[2]  P. P. Vaidyanathan,et al.  Effects of Multirate Systems on the Statistical Properties of Random Signals , 1993, IEEE Trans. Signal Process..

[3]  Zoran Cvetkovic,et al.  Nonuniform oversampled filter banks for audio signal processing , 2003, IEEE Trans. Speech Audio Process..

[4]  R. Haddad,et al.  Multiresolution Signal Decomposition: Transforms, Subbands, and Wavelets , 1992 .

[5]  G. Goodwin,et al.  Finite constraint set receding horizon quadratic control , 2004 .

[6]  Ingegneria dell’Informazione,et al.  Multiparametric Nonlinear Integer Programming and Explicit Quantized Optimal Control , 2003 .

[7]  Graham C. Goodwin,et al.  Finite Alphabet Control and Estimation , 2003 .

[8]  Orla Feely,et al.  A tutorial introduction to non‐linear dynamics and chaos and their application to sigma–delta modulators , 1997 .

[9]  D. Delchamps.  Nonlinear dynamics of oversampling A-to-D converters , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[10]  Graham C. Goodwin,et al.  Moving horizon optimal quantizer for audio signals , 2003 .

[11]  P. Ramadge.  On the periodicity of symbolic observations of piecewise smooth discrete-time systems , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[12]  Martin Vetterli,et al.  Oversampled filter banks , 1998, IEEE Trans. Signal Process..

[13]  Helmut Bölcskei,et al.  Noise reduction in oversampled filter banks using predictive quantization , 2001, IEEE Trans. Inf. Theory.

[14]  P. Vaidyanathan.  Multirate Systems And Filter Banks , 1992 .

[15]  Allen Gersho,et al.  Vector quantization and signal compression , 1991, The Kluwer international series in engineering and computer science.

[16]  Jan M. Maciejowski,et al.  Predictive control : with constraints , 2002 .

[17]  N. J. Fliege,et al.  Multirate Digital Signal Processing: Multirate Systems, Filter Banks, Wavelets , 1994 .

[18]  Helmut Bölcskei,et al.  Frame-theoretic analysis of oversampled filter banks , 1998, IEEE Trans. Signal Process..

[19]  S. Biyiksiz,et al.  Multirate digital signal processing , 1985, Proceedings of the IEEE.

[20]  Truong Q. Nguyen,et al.  Wavelets and filter banks , 1996 .

[21]  David Q. Mayne,et al.  Constrained model predictive control: Stability and optimality , 2000, Autom..

[22]  R. Schreier,et al.  Delta-sigma data converters : theory, design, and simulation , 1997 .

[23]  G. Goodwin,et al.  Audio quantization from a receding horizon control perspective , 2003, Proceedings of the 2003 American Control Conference, 2003..

[24]  John Vanderkooy,et al.  Quantization and Dither: A Theoretical Survey , 1992 .