Quantization of Filter Bank Frame Expansions Through Moving Horizon Optimization

This paper describes a novel approach to quantization in oversampled filter banks. The new technique is based on moving horizon optimization, does not rely on an additive white noise quantization model and allows stability to be explicitly enforced in the associated nonlinear feedback loop. Moreover, the quantization structure proposed here includes SigmaDelta and linear predictive subband quantizers as a special case and, in general, outperforms them.

[1]  Richard A. Haddad,et al.  Modeling, analysis, and optimum design of quantized M-band filter banks , 1995, IEEE Trans. Signal Process..

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

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

[4]  S. Tewksbury,et al.  Oversampled, linear predictive and noise-shaping coders of order N g 1 , 1978 .

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

[6]  Orla Feely.  Nonlinear dynamics of discrete-time circuits: A survey , 2007, Int. J. Circuit Theory Appl..

[7]  Bor-Sen Chen,et al.  Optimal signal reconstruction in noisy filter bank systems: multirate Kalman synthesis filtering approach , 1995, IEEE Trans. Signal Process..

[8]  Thomas Kailath,et al.  Linear Systems , 1980 .

[9]  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,.

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

[11]  J. Benedetto,et al.  Second-order Sigma–Delta (ΣΔ) quantization of finite frame expansions , 2006 .

[12]  John J. Benedetto,et al.  Sigma-delta quantization and finite frames , 2004, ICASSP.

[13]  Jeng-Shyang Pan,et al.  An efficient encoding algorithm for vector quantization based on subvector technique , 2003, IEEE Trans. Image Process..

[14]  Jelena Kovacevic,et al.  Wavelets and Subband Coding , 2013, Prentice Hall Signal Processing Series.

[15]  Graham C. Goodwin,et al.  Moving horizon design of discrete coefficient FIR filters , 2005, IEEE Transactions on Signal Processing.

[16]  David L. Neuhoff,et al.  The validity of the additive noise model for uniform scalar quantizers , 2005, IEEE Transactions on Information Theory.

[17]  Graham C. Goodwin,et al.  Multistep optimal analog-to-digital conversion , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

[18]  John J. Benedetto,et al.  Sigma-delta (/spl Sigma//spl Delta/) quantization and finite frames , 2006, IEEE Trans. Inf. Theory.

[19]  Peter H. Westerink,et al.  Scalar quantization error analysis for image subband coding using QMFs , 1992, IEEE Trans. Signal Process..

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

[21]  Robert J. Safranek,et al.  Signal compression based on models of human perception , 1993, Proc. IEEE.

[22]  Helmut Bölcskei,et al.  Orthogonalization of OFDM/OQAM pulse shaping filters using the discrete Zak transform , 2003, Signal Process..

[23]  M. Arunkumar,et al.  Minimization of quantization noise amplification in biorthogonal subband coders , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[24]  P. P. Vaidyanathan,et al.  Linear phase cosine modulated maximally decimated filter banks with perfect reconstruction , 1994, Proceedings of IEEE International Symposium on Circuits and Systems - ISCAS '94.

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

[26]  P. P. Vaidyanathan,et al.  Cosine-modulated FIR filter banks satisfying perfect reconstruction , 1992, IEEE Trans. Signal Process..

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

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

[29]  Thomas Kailath,et al.  On robust signal reconstruction in noisy filter banks , 2005, Signal Process..

[30]  I. Daubechies,et al.  Approximating a bandlimited function using very coarsely quantized data: A family of stable sigma-delta modulators of arbitrary order , 2003 .

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

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

[33]  Gabor C. Temes,et al.  Oversampled, Linear Predictive and NoiseShaping Coders of Order N , 1992 .

[34]  Petros G. Voulgaris,et al.  On optimal ℓ∞ to ℓ∞ filtering , 1995, Autom..

[35]  E QuevedoDaniel,et al.  Quantization of filter bank frame expansions through moving horizon optimization , 2009 .

[36]  G. David Forney,et al.  Maximum-likelihood sequence estimation of digital sequences in the presence of intersymbol interference , 1972, IEEE Trans. Inf. Theory.

[37]  Orla Feely.  Nonlinear dynamics of discrete-time circuits: A survey: Research Articles , 2007 .

[38]  F. Hlawatsch,et al.  Oversampled cosine modulated filter banks with perfect reconstruction , 1998 .

[39]  Koji Kotani,et al.  A unified projection method for fast search of vector quantization , 2004, IEEE Signal Processing Letters.

[40]  Alexander M. Powell,et al.  Coarsely Quantized Redundant Representations of Signals , 2006 .

[41]  Terri S. Fiez,et al.  A comparative analysis of parallel delta-sigma ADC architectures , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[42]  C. Sinan Güntürk,et al.  Refined error analysis in second-order Sigma-Delta modulation with constant inputs , 2004, IEEE Trans. Inf. Theory.

[43]  Graham C. Goodwin,et al.  Constrained Control and Estimation: an Optimization Approach , 2004, IEEE Transactions on Automatic Control.

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

[45]  David J. Sakrison,et al.  The effects of a visual fidelity criterion of the encoding of images , 1974, IEEE Trans. Inf. Theory.

[46]  Bor-Sen Chen,et al.  Minimax deconvolution design of multirate systems with channel noises: a unified approach , 1999, IEEE Trans. Signal Process..

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

[48]  Tapio Saramäki,et al.  Design of practically perfect-reconstruction cosine-modulated filter banks: a second-order cone programming approach , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[49]  Graham C. Goodwin,et al.  On Optimal Perfect Reconstruction Feedback Quantizers , 2008, IEEE Transactions on Signal Processing.

[50]  Graham C. Goodwin,et al.  Multistep Detector for Linear ISI-Channels Incorporating Degrees of Belief in Past Estimates , 2007, IEEE Transactions on Communications.

[51]  Ronald A. DeVore,et al.  A/D conversion with imperfect quantizers , 2006, IEEE Transactions on Information Theory.

[52]  Graham C. Goodwin,et al.  Constrained Control and Estimation , 2005 .