Chair: Thomas P. Barnwell, Georgia Institute of Technology, (USA)
Bo Xuan, Washington State University (USA)
Roberto H. Bamberger, Washington State University (USA)
This paper presents a generalization of the one-dimensional principal component filter bank (PCFB) derived in [4] to higher dimensions. Previously, the results in [4] were extended to two-dimensional signals in [5], but the work in [5] was limited to 2D signals and separable resampling operators. The filter bank discussed here results in minimizing the mean squared error when only Q out of P subbands are retained. Furthermore, it is shown that the filter bank maximizes theoretical coding gain (TCG). Simulations are presented demonstrating the potential of the PCFB.
Masoud R.K. Khansari, University of California at Berkeley (USA)
Eric Dubois, INRS - Telecommunications (CANADA)
We show how the Pade table can be utilized to develop a new lattice structure for general two-channel bi-orthogonal perfect reconstruction (PR) filter banks. This is achieved through characterization of all two-channel bi- orthogonal PR filter banks. The parameter space found using this method is unique for each filter bank. Similarly to any other lattice structure, the PR property is achieved structurally and quantization of the parameters of the lattice does not effect this property. Furthermore, we demonstrate that for a given filter, the set of all complementary filters can be uniquely specified by two parameters, namely the end- to-end delay of the system and a scalar quantity.
Peter N. Heller, Aware Inc.
Truong Q. Nguyen, University of Wisconsin
Hemant Singh, Aware Inc. (USA)
W. Knox Carey, Aware Inc. (USA)
This paper investigates the design of M-band linear phase wavelet filter banks (M > 2), and explores their application to image coding. The generalized LOT description of M-band linear-phase paraunitary filter banks is used to parametrize the M-band linear-phase orthogonal wavelets. It is proven that an M-band linear-phase orthogonal wavelet of even length cannot have more than one vanishing moment. Since this limits the effectiveness of the resulting wavelet filters, we next suggest methods for the construction of linear-phase biorthogonal M- band wavelet lowpass filters, generalizing prior 2-band constructions. However, one cannot guarantee that an arbitrary lowpass filter pair can be completed to a full perfect-reconstruction filter bank. Finally, the new linear-phase orthogonal wavelet filter banks are applied to image compression and their performance is compared with known wavelet filters.
M.J. Grimble, Industrial Control Centre University of Strathclyde (UK)
A new approach to linear estimation in time-varying discrete multivariable systems is described. The signal model is taken to be a time-varying vector difference equation which can be expressed in ARMA polynomial system form. An optimal linear filter and predictor is derived in terms of time-dependent polynomial operators and this can also be implemented as a recursive algorithm using difference equations. The system model and filter are particularly relevant in self-tuning filtering applications.
X. Shen, University of Waterloo (CANADA)
L. Deng, University of Waterloo (CANADA)
In this paper, discrete H-infinity filter design with a linear quadratic (LQ) game approach is presented. The exogenous inputs composed of the hostile noise signals and system initial condition are assumed to be finite energy signals with unknown statistics. The design criterion is to minimize the worst possible amplification of the estimation error signal, which is different from the classical minimum variance estimation error criterion for the modified Wiener or Kalman filter design. The approach can show that how far the estimation error can be reduced under an existence condition on the solution to a corresponding Riccati equation. The application of the discrete H-infinity filter to enhance speech contaminated by additive noise is then investigated. In the H-infinity estimation, the noise sources can be arbitrary signals with only requirement of bounded energy, this estimation is more appropriate in the practical speech enhancement.
S.C.Chan, University of Hong Kong (HONG KONG)
This paper proposes a new family of perfect reconstruction (PR) linear phase filter banks called the generalized lapped transform (GLT). The GLT differs from the traditional lapped orthogonal transform (LOT) [1] in that it is nonorthogonal and hence offers more freedom to avoid blocking effects and improve the coding gain. Since the GLT can also be viewed as a generalization of the traditional discrete cosine transform (DCT), fast algorithms [2-4] for their implementation are also available.
S. Basu, Stevens Institute of Technology (USA)
H.M. Choi, Stevens Institute of Technology (USA)
Complete parameterization of multiband linear phase biorthogonal filter banks are given. The method uses matrix reduction methods similar to the Hermite reduction method of linear system theory. Computational algorithms are derived for design, and examples are worked out.
Cormac Herley, Hewlett-Packard Laboratories
Zixiang Xiong, University of Illinois at Urbana- Champaign (USA)
Kannan Ramchandran, University of Illinois at Urbana- Champaign (USA)
Michael T. Orchard, University of Illinois at Urbana- Champaign (USA)
We examine the question of how to choose a time-varying filter bank representation for a signal which is optimal with respect to an additive cost function. We present in detail an efficient algorithm for the Haar filter set which finds the optimal basis, given the constraint that the time and frequency segmentations are binary. Extension to multiple dimensions is simple, and use of arbitrary filter sets is also possible. We verify that the algorithm indeed produces a lower cost respresentation than any of the wavelet packet respresentations for compression of images using a simple Rate-Distotion cost.
Sheila S. Hemami, Cornell University
Robert M. Gray, Stanford University (USA)
Packet-based transmission of subband coded images over lossy networks presents a reconstruction problem at the decoder. Accurate reconstruction of the high-energy low frequency subband coefficients is imperative in providing consumer-grade image quality. This paper introduces a family of one-dimensional quadrature mirror filters (QMFs) designed to minimize the mean-squared error of reconstructed low frequency coefficients for a given reconstruction algorithm to be implemented at the decoder. Mean-reconstruction, in which a missing coefficient is replaced with the average of its neighbors either horizontally or vertically, is selected for its simplicity and implementation ease. The resulting filters perform well as QMFs and provide the desired reconstruction properties in the event of loss. While the filters are developed using mean-reconstruction, the filter design algorithm can be used with more sophisticated reconstruction techniques, providing that the mean-squared error can be expressed in the appropriate quadratic form.
Vesa Valimaki, Helsinki University of Technology (FINLAND)
Matti Karjalainen, Helsinki University of Technology (FINLAND)
This paper discusses a discrete-time modeling technique where the length of time delays can be arbitrarily adjusted. The new system is called a fractional delay waveguide model (FDWM). Formerly, FDWMs have only been implemented with FIR-type fractional delay filters. We show how an FDWM can be implemented using allpass filters. We use low-order allpass filters that are maximally-flat approximations of the ideal delay. The advantages of the allpass approach are computational efficiency and reduced approximation error. The proposed structure can be applied to discrete-time modeling of acoustic tubes, such as the human vocal tract or resonators of musical instruments.