1:00, SPTM-L4.1
AN ITERATIVE SOLUTION FOR THE OPTIMAL POLES IN A KAUTZ SERIES
B. SARROUKH, S. VAN EIJNDHOVEN, A. DEN BRINKER
Kautz series allow orthogonal series expansion of finite-energy signals defined on a semi-infinite axis. The Kautz series consists of orthogonalized exponential functions or sequences. This series has as free parameters an ordered set of poles, each pole associated with an exponential function or sequence. For reasons of approximation and compact representation (coding), an appropriate set of ordered poles is therefore convenient. An iterative procedure to establish the optimal parameters according to an enforced convergence criterion is introduced.

1:20, SPTM-L4.2
VARYING-RADIX NUMERATION SYSTEM AND ITS APPLICATIONS
X. FAN, Y. SU, R. YANG
At present, there are no effective methods for modeling on representing sequence containing position information in some special problems. A novel varying-radix numeration system is proposed to solve this kind of problems. This varying-radix numeration system differs from common fixed radixes numeration systems. The applications of varying-radix numeration system in a First-In-Last-Out (FILO) stack problem and Multi-Pulse Excited Linear Prediction (MPELP) vocoder have illustrated the availability and benefit of this specific numeration system.

1:40, SPTM-L4.3
DYNAMIC COMPONENTS OF LINEAR STABLE MIXTURES FROM FRACTIONAL LOW ORDER MOMENTS
T. FABRICIUS, P. KIDMOSE, L. HANSEN
The second moment based independent component analysis scheme of Molgedey and Schuster is generalized to fractional low order moments, relevant for linear mixtures of heavy tail stable processes. The Molgedey and Schuster algorithm stands out by allowing explicitly construction of the independent components. Surpricingly, this turns out to be possible also for decorrelation based on fractional low order moments. Keywords: Blind Source Separation (BSS), Dynamic Components, Independent Component Analysis (ICA), Stable process, Fractional lower order moments, Cocktail party problem

2:00, SPTM-L4.4
PEAK LOCATIONS IN ALL-PASS SIGNALS - THE MAKHOUL CONJECTURE CHALLENGE
R. RAJAGOPAL, L. WENZEL
In [1] the Makhoul Conjecture Challenge was published. To answer was the question whether or not the location of the peak of a digital stable all-pass filter lies in [0, 2p-1], where p is the order of the all-pass filter. In this paper we construct numerous counter-examples, prove a new theorem stating that there is at least an upper bound on the order of p3/2 for the location of the peak, and discuss the algebraic structure of all-pass filters and their impulse responses. The paper is heavily based on an experimental approach. [1] J. Makhoul, Conjectures on the peaks of all-pass signals, IEEE Signal Processing Magazine, vol. 17, no. 3, pp. 8-11, May 2000

2:20, SPTM-L4.5
MAKHOUL'S CONJECTURE FOR P=2
N. BOSTON
Last year, the IEEE Signal Processing Society offered a prize of \$1000 for prov ing or disproving Makhoul's conjecture, which says that, given a causal all-pass digital signal $x_n$ of order $p$, with nonzero $x_0$, the location of the peak of $x_n$ always lies between $n = 0$ and $n = 2p-1$. The case of $p = 1$ is tri vial, and no further progress had been made in $25$ years until Lertniphonphun, Rajagopal, and Wenzel gave counterexamples for large $p$. In this paper, Makhoul's conjecture is proven for $p = 2$. It is also shown that the conjecture fails dramatically in the case of complex coefficients.

2:40, SPTM-L4.6
CHARACTERIZATION OF SELF-SIMILARITY PROPERTIES OF DISCRETE-TIME LINEAR SCALE-INVARIANT SYSTEMS
S. LEE, R. RAO, R. NARASIMHA
Discrete-time linear systems that possess scale-invariance properties even in the presence of continuous dilation were proposed by Zhao and Rao. The principal purpose of this article is to describe results of subsequent investigation which have led to characterization of self-similarity properties of discrete-time signals synthesized by these systems. It is shown that white noise inputs to these linear scale invariant systems, which are unique in DSP literature, produce self similar outputs regardless of the marginal distribution of the noise. In most instances the output is fractional Gaussian. For havey tailed input distributions, the output is also havey-tailed and self-similar. It si also shown that it is possible to synthesize statistically self-similar signals whose self-similarity parameters are consistent with those observed in network traffic.