1:00, SPTM-P1.1
SAMPLING CRITERION FOR NONLINEAR SYSTEMS WITH A BANDPASS INPUT
C. TSENG
Sampling requirements for nonlinear systems with a bandpass input are developed in this paper. It is well known that the output of a nonlinear system may have a larger bandwidth than that of the input. According to the Nyquist sampling theorem, the sampling rate needs to be at least twice the maximum frequency of the output to avoid aliasing. However, if the input is a bandpass signal, the spectrum of the output is usually distributed over several frequency bands. In this case, using the bandpass sampling concept, it is possible to sample the output at a much lower rate. In this paper, conditions for such a lower sampling rate to exist are derived for nonlinear systems up to the third order. Supporting computer simulation is also provided.

1:00, SPTM-P1.2
THE SQUARE-ROOT UNSCENTED KALMAN FILTER FOR STATE AND PARAMETER-ESTIMATION
R. VAN DER MERWE, E. WAN
Over the last 20-30 years, the extended Kalman filter (EKF) has become the algorithm of choice in numerous nonlinear estimation and machine learning applications. The EKF applies the standard linear Kalman filter methodology to a linearization of the true nonlinear system. This approach is sub-optimal, and can easily lead to divergence. Julier et al. proposed the unscented Kalman filter (UKF) as a derivative-free alternative to the extended Kalman filter in the framework of state-estimation. This was extended to parameter-estimation by Wan and van der Merwe. The UKF consistently outperforms the EKF at an equal computational complexity of O(L^3). When the EKF is applied to parameter-estimation, an O(L^2) implementation is possible. This paper introduces the square-root unscented Kalman filter (SR-UKF) which is also O(L^3) for state-estimation and O(L^2) for parameter estimation. In addition, the square-root forms have the added benefit of numerical stability and guaranteed positive semi-definiteness of the state covariances.

1:00, SPTM-P1.3
GAUSSIAN SUM PARTICLE FILTERING FOR DYNAMIC STATE SPACE MODELS
J. KOTECHA, P. DJURIC
For dynamic systems, sequential Bayesian estimation requires updating of the filtering and predictive densities. For nonlinear and non-Gaussian models, sequential updating is not straightforward, as in the linear Gaussian model. In this paper, densities are approximated as finite mixture models as is done in the Gaussian sum filter. A novel method is presented, whereby sequential updating of the filtering and posterior densities is performed by particle based sampling methods. The filtering method has combined advantages of Gaussian sum and particle based filters and simulations show that the presented filter can outperform both methods.

1:00, SPTM-P1.4
SIGNAL PROCESSING USING LUT FILTERS BASED ON HIERARCHICAL VQ
R. DE QUEIROZ, P. FLECKENSTEIN
Vector quantization (VQ) is a powerful tool in signal processing. Hierarchical VQ (HVQ) is a method to implement VQ completely based on look-up tables (LUT). In HVQ, both encoders and decoders are inherently simple and fast, since there are no searches over codebooks. We introduce an overlapped HVQ (OHVQ) method, in which the number of samples is preserved after each HVQ stage. After the last stage, each OHVQ code in a particular location in the signal will map to a block (vector) which approximates that neighbourhood in the original sequence. For this reason, OHVQ is used as a basis to create a LUT-based filter, i.e. a spatial signal processor with very fast implementation. Preliminary analysis and image processing examples are shown demonstrating the efficiency of the proposed method.

1:00, SPTM-P1.5
NONPARAMETRIC ESTIMATORS FOR ONLINE SIGNATURE AUTHENTICATION
A. IHLER, J. FISHER III, A. WILLSKY
We present extensions to our previous work in modelling dynamical processes. The approach uses an information theoretic criterion for searching over subspaces of the past observations, combined with a nonparametric density characterizing its relation to one-step-ahead prediction and uncertainty. We use this methodology to model handwriting stroke data, specifically signatures, as a dynamical system and show that it is possible to learn a model capturing their dynamics for use either in synthesizing realistic signatures and in discriminating between signatures and forgeries even though no forgeries have been used in constructing the model. This novel approach yields promising results even for small training sets.

1:00, SPTM-P1.6
CHAOTIC AR(1) MODEL ESTIMATION
C. PANTALEON, D. LUENGO, I. SANTAMARIA
Chaotic signals generated by iterating nonlinear difference equations may be useful models for many natural phenomena. In this paper we propose a family of chaotic models for signal processing applications. The chaotic signals generated by this family of first order difference equations have autocorrelations identical to stochastic first-order autoregressive (AR) processes. After considering the huge computational cost and the inconsistency of the optimal model estimator in the maximum-likelihood (ML) sense we propose low cost, suboptimal estimation approaches. Computer simulations show the good performance of the proposed modeling approach.

1:00, SPTM-P1.7
AN IMPROVED ENERGY DEMODULATION ALGORITHM USING SPLINES
D. DIMITRIADIS, P. MARAGOS
A new algorithm is proposed for demodulating discrete-time AM-FM signals, which first interpolates these signals with smooth splines and then uses the continuous-time energy separation algorithm (ESA) based on the Teager-Kaiser energy operator. This Spline-based ESA retains the excellent time resolution of the former ESAs but provides additional robustness in the presence of noise.

1:00, SPTM-P1.8
INTEGER FAST FOURIER TRANSFORM (INTFFT)
S. ORAINTARA, Y. CHEN, T. NGUYEN
In this paper, a concept of integer fast Fourier transform (IntFFT) for approximating the discrete Fourier transform is introduced. Unlike the fixed-point fast Fourier transform (FxpFFT), the new transform has properties that it is an integer-to-integer mapping, power adaptable and also reversible. Lifting scheme is used to approximate complex multiplications appearing in the FFT lattice structures. Split-radix FFT is used to illustrate the approach for the case of 2^N-point FFT. The transform can be implemented by using only bit shifts and additions but no multiplication. While preserving the reversibility, the IntFFT is shown experimentally to yield the same accuracy as the FxpFFT when their coefficients are quantized to a certain number of bits. Complexity of the IntFFT is shown to be much lower than that of the FxpFFT in terms of the numbers of additions and shifts.

1:00, SPTM-P1.9
A TRUE STOCHASTIC GRADIENT ADAPTIVE ALGORITHM FOR APPLICATIONS USING NONLINEAR ACTUATORS
M. COSTA, J. BERMUDEZ
This work considers the practical situation where adaptive systems are subject to a saturation nonlinearity at the output of the adaptive filter. Such is the case in active control of noise and vibration. A new adaptive algorithm is proposed which implements the true stochastic gradient approach to the nonlinear problem. Deterministic nonlinear recursions are derived which model the mean weight and mean square error behaviors. The steady-state behavior is also studied. The practical aspects of nonlinearity estimation and hardware implementation are addressed. It is shown that the new algorithm outperforms the LMS algorithm even for considerable errors in estimating the nonlinearity parameters.