Chair: Ali Akansu, New Jersey Institute of Technology, (USA)
Shuichi Ohno, Kyoto University (JAPAN)
Hideaki Sakai, Kyoto University (JAPAN)
Generally, the output of a filter bank for a stationary input signal is not stationary but cyclostationary. In this paper, by using cyclostationary spectral analysis, the spectral correlation density of this output is derived. Using this result we derive a criterion to construct an optimal 2-band perfect reconstruction filter bank which minimizes the averaged mean squared reconstruction error when the high pass band signal is dropped. By adding constrains to the filter coefficients, the biorthogonal filter bank, the conjugate quadrature filter bank and the biorthogonal linear phase filter bank are respectively obtained. Some numerical results are also presented for optimal biorthogonal and PR linear phase filter banks which are compared in terms of some performance measures.
Ricardo L. de Queiroz, Xerox Corporation
K.R. Rao, University of Texas at Arlington (USA)
The use of a paraunitary filter bank for image processing requires a special treatment at image boundaries to ensure perfect reconstruction and orthogonality of these regions. Using time-varying boundary filter banks, we will discuss a procedure that explores all degrees of freedom of the border filters in a method essentially independent of signal extensions, allowing us to design optimal boundary filter banks, while maintaining fast implementation algorithms.
Parviz Saghizadeh, University of California at Los Angeles (USA)
Alan N. Willson Jr., University of California at Los Angeles (USA)
A generic approach is presented for the design of uniform-band M-channel (M >= 2) perfect-reconstruction FIR filter banks employing linear-phase analysis and synthesis filters. The technique designs on the impulse responses of the analysis filters directly. The design problem is formulated as a quadratic programming problem. The perfect-reconstruction feature of the filter bank can either be implicitly enforced through a set of mathematical relationships among the analysis filters' coefficients, or through a set of constraints in the optimization program. The former approach results in a filter bank whose PR (perfect reconstruction) feature's dependency on hardware and software is eliminated or, at least minimized. The criterion for optimality is least-squares.
Timo I. Laakso, University of Westminster (UK)
Vesa Valimaki, Helsinki University of Technology
Jukka Henriksson, Nokia Research Center (FINLAND)
An efficient technique for sampling rate conversion for arbitrary (incommensurate) ratios is proposed. The technique is based on fractional delay filters that are efficient to implement and that can be controlled with a small number of arithmetic operations per output sample. We consider an application in digital television (DTV) transmission where, according to present standard proposals, conversions between several incommensurate sampling rates must be possible. Rather than trying to design separate fixed filters for each possible conversion, we outline a system which may be tuned for any possible downsampling ratio. A sampling rate conversion system based on the straightforward and simple Lagrange interpolation technique is illustrated, with a novel and highly efficient implementation structure. Various error sources involved are analyzed and a mean-square-error (MSE) type cost function is defined to aid in the system design.
W.M. Campbell, Cornell University (USA)
T.W. Parks, Cornell University (USA)
The design of rate-changing multirate systems using a maximum relative $l^2$-error criterion is analyzed. Using multirate techniques, the criterion is simplified to a matrix-response approximation problem. An algorithm using convex optimization is proposed to solve the problem. An example illustrates the use of the algorithm and effectiveness over methods intended for LTI system design.
Pierre Moulin, Bell Communication Research (USA)
The design of a quadrature--mirror filter (QMF) bank $(H,G)$ adapted to input signal statistics is considered. The adaptation criterion is maximization of the coding gain and has so far been viewed as a difficult nonlinear constrained optimization problem. In this paper, it is shown that in fact the coding gain depends only upon the product filter $P(z) = H(z) H(z^{-1})$. The optimization problem formulated in terms of the coefficients of $P(z)$ gives rise to a linear semi--infinite program (SIP). A simple SIP algorithm using a discretization method is presented. The filter $H(z)$ is obtained by deflation and spectral factorization of $P(z)$.
Alfred Mertins, Hamburg University of Technology (GERMANY)
In this paper, methods for switching filter coefficients and filter bank structures and methods for processing finite length signals will be studied. The problem of designing optimal boundary and transition filters will be solved directly via singular value decomposition (SVD) while the optimality criterion is based on the subband statistics. The optimized filters provide a good match between the subband statistics in transition regions (and at the boundaries) to the statistics in steady state. The filter banks considered are maximally decimated M-channel linear and non-linear phase (biorthogonal and paraunitary) filter banks with real filter coefficients.
Innho Jee, Polytechnic University (USA)
R.A. Haddad, Polytechnic University (USA)
This paper demonstrates that the scalar non-linear gain-plus-additive noise quantization model can be used to represent each vector quantizer in an M-band subband codec. The validity and accuracy of this analytic model is confirmed by comparing the calculated model quantization errors with actual simulation of the optimum LBG vector quantizer. We compute the mean squared reconstruction error(MSE) which depends on N the number of entries in each codebook, k the length of each codeword, and on the filter bank coefficients. We form this MSE measure in terms of the equivalent scalar quantization model and find the optimum FIR filter coefficients for each channel in the M-band structure for a given bit rate, given filter length, and given input signal correlation model. Specific design examples are worked out for a 4-tap filter in a two-band paraunitary structure. Theoretical results are confirmed by extensive Monte Carlo simulation.
B. Tang, University of California at Los Angeles (USA)
A. Shen, University of California at Los Angeles (USA)
G. Pottie, University of California at Los Angeles (USA)
A. Alwan, University of California at Los Angeles (USA)
In this study, a methodology for transform-based spectral analysis of subband filtered signals is developed. The methodology is based on performing the analysis on subband samples instead of on the input signal directly. Aliasing due to decimation is eliminated by including the effects of the adjacent subband in the analysis of frequencies near the filterbank transition regions. The frequency resolution and spectral leakage is nearly the same as if the transform had been performed on the input directly. In an M band filterbank, the analysis block length is reduced by a factor of M. This reduces the complexity of source compression techniques based on subband decomposition and spectral analysis, such as the high quality speech coder we are developing and the ISO/MPEG audio codec.
Joel Mau, France Telecom (FRANCE)
Jacques Valot, France Telecom (FRANCE)
Damien Minaud, France Telecom (FRANCE)
We present a solution for the construction of orthogonal time-varying filter banks without transient filters. To reach this result the idea is the following: all the various filter banks used in the time-varying decomposition are not arbitrary, but are linked together and in fact are derived from an unique initial orthogonal filter bank. With this new technique, the PR property is always guaranteed even if we switch abruptly from one filter bank to an other without the use of transient filters. We will explain, by taking an initial M-band orthogonal filter bank which performs a regular M-band frequency splitting, how to derive various mutually orthogonal filter banks with almost any arbitrary time/frequency resolution, even able to perform irregular frequency splitting like for example in a wavelet decomposition.