Chair: Mark J.T. Smith, Georgia Institute of Technology (USA)
P. P. Vaidyanathan, California Institute of Technology (USA)
See-May Phoong, California Institute of Technology (USA)
If a discrete time signal x(n) is bandlimited appropriately we can decimate it without aliasing. However, there exists a broad class of non bandlimited signals which can be recovered perfectly from their decimated versions. In this paper we consider both uniform and nonuniform decimation of this kind and explore some applications, especially in noise shaping and in Sigma-Delta modulator type architectures.
Brian Foster, National University of Ireland (IRELAND)
Cormac Herley, Hewlett Packard Laboratories (USA)
We examine the problem of reconstructing a discrete-time signal given only $n$ of its $M$-phase components. Borrowing analysis from the field of perfect reconstruction filter banks enables us to derive necessary and sufficient conditions under which reconstruction is possible. Essentially, in a perfect reconstruction system, the conditions to reconstruct from partial information are equivalent to the conditions to ensure that the rest of the information does not contribute to the reconstructed signal. An application is that this allows us to reconstruct multiband signals which have overall bandwidth of no more than $B$, yet cannot be reconstructed from uniformly spaced spaced samples at the minimum rate $1/2B$.
Zoran Cvetkovic, University of California - Berkeley (USA)
The subject of this study is paraunitary modulated filter banks. A factorization of the polyphase matrices of these filter banks, which is described here, gives complete characterization of tight Gabor frames in $l^2(Z)$, with arbitrary rational oversampling ratios. Tight Gabor frames, being less constrained than orthogonal bases, allow for filter bank designs with good localization in both time and frequency.
Phillip A. Regalia, Institut National des Telecommunications (FRANCE)
Dong-Yan Huang, Institut National des Telecommunications (FRANCE)
We consider the problem of adaptively optimizing a two-channel lossless FIR filter bank, which finds application in subband coding or wavelet signal analysis. Instead of using a gradient descent procedure---with its inherent problem of possible convergence to local minima---we consider two eigenstructure algorithms. Both algorithms feature a priori bounds on the output error variance at any convergent point, and based on simulations lead to solutions that lie acceptably close to a global minimum point of an output error cost function.
T. Cooklev, Tokyo Institute of Technology (JAPAN)
A. Nishihara, Tokyo Institute of Technology (JAPAN)
T. Yoshida, Tokyo Institute of Technology (JAPAN)
M. Sablatash, Communications Research Centre (CANADA)
In this paper design methods for regular multidimensional perfect reconstruction (PR) filter banks are described. A systematic method for two- channel and four-channel filter banks is presented. The main novelties are: (1) the filters have impulse response with square support, rather than diamond support; (2) regular designs that have rectangular support are also presented, which are highly efficient in practice, since expensive memory is saved; (3) in addition to new diamond filters for the two-channel case, hexagonally-symmetric filters are also derived; and (4) novel 3-D filter banks are also designed. In all cases the filters are linear phase, achieve arbitrarily high regularity and can be used to obtain biorthogonal wavelet bases. The filter banks can be implemented in a structurally perfect-reconstruction manner.
Masaaki Ikehara, Keio University (JAPAN)
In this paper, I consider about the theory of modulated 2 Dimensional (2-D) perfect reconstruction (PR) filters banks with permissible passbands. At first, I design a 2-D complex digital filter with half passband obtained by the sampling matrix. Next, 2-D analysis filter banks are realized by modulating this prototype 2-D complex digital filter and by taking the real part of the output. It is also shown that the modulation in 2-D frequency plane is equivalent to 1-D DFT. A necessary and sufficient condition for 2-D perfect reconstruction filter banks is derived. Finnaly I show some examples.
Gerald Schuller, Georgia Institute of Technology (USA)
Mark J. T. Smith, Georgia Institute of Technology (USA)
Historically, exact reconstruction FIR filter banks have had system delays of L-1, where L is the length of the analysis and synthesis filters. Recently is was shown that the system delay could be made less than L-1, which is attractive in applications like speech coding where excessive delays are annoying. In this paper, a formulation and new design algorithm are introduced for two-band low-delay filter banks. The formulation is related to that of two-band lattice filter banks and provides a broad range of design flexibility within a compact framework. Both exact reconstruction and specified system delay are guaranteed by the structure of the framework.
Gerardo Gonzalez-Rosiles, The University of Texas at El Paso (USA)
Sergio D. Cabrera, The University of Texas at El Paso (USA)
Sing- Wai Wu, The University of Texas at El Paso (USA)
This paper deals with the recovery of an image when some partially redundant subband data has been irreversibly corrupted. The approach presented assumes an overcomplete subband decomposition and uses a local Optimal Recovery estimator that works as a block processing scheme. The method takes advantage of the inherent correlation and redundancy among the remaining uncorrupted subband data. We view this approach as an alternative or as a complementary method to be used with forward error correcting codes requiring only error detection capability. We test the performance using row/column separable processing on images.
Francois Moreau de Saint-Martin, CCETT
Albert Cohen, CEREMADE Universite Paris-Dauphine
Pierre Siohan, CCETT (FRANCE)
We study the non-orthogonality of perfect-reconstruction (PR) biorthogonal filter banks by measuring the energy preservation between the spatial and transform domains. The mathematical formulation of that issue leads to the computation of the Riesz constants, and a more relevant modelization leads to a measure of near-orthogonality which is well suited for image compression systems based on filter banks. This provides a criterion for the validity of the energy preservation approximation: we can compare the latter approximation with the one that is made when estimating the perceptual quality of an image by the mean square error.
Michail K. Tsatsanis, University of Virginia (USA)
Georgios B. Giannakis, University of Virginia (USA)
Direct sequence, code-division multiple access (CDMA) schemes offer an attractive alternative for sharing a transmission medium among many users, while requiring minimal co-operation among them. A number of signal processing issues are related to the receiver's task of multiuser information extraction and detection. In this paper, a discrete-time multirate formulation is introduced for asynchronous CDMA systems, which can incorporate multipath effects. In this framework, linear receivers are derived which can completely suppress multiuser interference (decorrelating receivers). A criterion is introduced , which guarantees the decorrelating property, while providing optimal solutions in the presence of noise. The synchronization problem in a multipath environment is also studied, and identifiability conditions are established. A subspace algorithm is proposed, to estimate the user's delays and multipath channels in a blind scenario.