Identification of linear periodically time-varying (LPTV) systems

A linear periodically time-varying (LPTV) system is a linear time-varying system with the coefficients changing periodically, which is widely used in control, communications, signal processing, and even circuit modeling. This thesis concentrates on identification of LPTV systems. To this end, the representations of LPTV systems are thoroughly reviewed. Identification methods are developed accordingly. The usefulness of the proposed identification methods is verified by the simulation results. A periodic input signal is applied to a finite impulse response (FIR)-LPTV system and measure the noise-contaminated output. Using such periodic inputs, we show that we can formulate the problem of identification of LPTV systems in the frequency domain. With the help of the discrete Fourier transform (DFT), the identification method reduces to finding the least-squares (LS) solution of a set of linear equations. A sufficient condition for the identifiability of LPTV systems is given, which can be used to find appropriate inputs for the purpose of identification. In the frequency domain, we show that the input and the output can be related by using the discrete Fourier transform (DFT) and a least-squares method can be used to identify the alias components. A lower bound on the mean square error (MSE) of the estimated alias components is given for FIR-LPTV systems. The optimal training signal achieving this lower MSE bound is designed subsequently. The algorithm is extended to the identification of infinite impulse response (IIR)-LPTV systems as well. Simulation results show the accuracy of the estimation and the efficiency of the optimal training signal design

A decimated electronic cochlea on a reconfigurable platform.

Wong Chun Kit.Thesis submitted in: October 2006.Thesis (M.Phil.)--Chinese University of Hong Kong, 2007.Includes bibliographical references (leaves 73-76).Abstracts in English and Chinese.Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Background and Motivation --- p.1Chapter 1.2 --- Objectives --- p.4Chapter 1.3 --- Contributions --- p.4Chapter 1.4 --- Thesis Outline --- p.5Chapter 2 --- Digital Signal Processing --- p.6Chapter 2.1 --- Introduction --- p.6Chapter 2.2 --- Discrete-time Signals and Systems --- p.7Chapter 2.2.1 --- Discrete-time Signals --- p.7Chapter 2.2.2 --- Discrete-time Signal Processing Systems --- p.9Chapter 2.2.3 --- Linear Time-Invariant (LTI) Systems --- p.10Chapter 2.3 --- Finite Impulse Response (FIR) Filters --- p.13Chapter 2.3.1 --- Introduction --- p.13Chapter 2.3.2 --- Windowing FIR Filter Design Method --- p.15Chapter 2.4 --- Infinite Impulse Response (IIR) Filters --- p.17Chapter 2.4.1 --- Introduction --- p.17Chapter 2.4.2 --- Bilinear Transform IIR Filter Design Method --- p.18Chapter 2.4.3 --- Spectral Transformations of IIR Filters --- p.22Chapter 2.5 --- Comparison on FIR and IIR Filters --- p.25Chapter 2.6 --- Digital Signal Resampling --- p.26Chapter 2.6.1 --- Introduction --- p.26Chapter 2.6.2 --- Resampling by Decimation --- p.26Chapter 2.6.3 --- Resampling by Interpolation --- p.28Chapter 2.6.4 --- Resampling by a Rational Factor --- p.29Chapter 2.7 --- Introduction to Dual Fixed-point (DFX) Representation --- p.30Chapter 2.8 --- Summary --- p.33Chapter 3 --- Lyon and Mead's Cochlea Model --- p.34Chapter 3.1 --- Introduction --- p.34Chapter 3.2 --- Digital Cochlea Model: Cascaded IIR Filters --- p.37Chapter 3.2.1 --- Introduction --- p.37Chapter 3.2.2 --- Bandwidth and Centre frequencies --- p.38Chapter 3.2.3 --- Zeros and Poles --- p.39Chapter 3.3 --- Modifications for Decimated Cochlea Model --- p.41Chapter 3.3.1 --- Introduction --- p.41Chapter 3.3.2 --- Aliasing Avoidance --- p.42Chapter 3.3.3 --- Coefficient Modification after Decimation --- p.43Chapter 3.4 --- Summary --- p.47Chapter 4 --- System Architecture --- p.48Chapter 4.1 --- Introduction --- p.48Chapter 4.2 --- Hardware Platform and CAD Tools --- p.48Chapter 4.3 --- Sequential Processing Electronic Cochlea --- p.51Chapter 4.3.1 --- Pipelining - An Interleaving Scheme --- p.53Chapter 4.3.2 --- Decimation in Sequential Processing Electronic Cochlea . --- p.54Chapter 4.3.3 --- Multiple Sequential Cores --- p.55Chapter 4.3.4 --- Architecture of the DFX Filter Computation Core --- p.55Chapter 4.4 --- Summary --- p.60Chapter 5 --- Experimental Results --- p.61Chapter 5.1 --- Introduction --- p.61Chapter 5.2 --- Testing Environment --- p.61Chapter 5.3 --- Performance of the Sequential Electronic Cochlea --- p.63Chapter 5.3.1 --- Comparisons --- p.63Chapter 5.4 --- Summary --- p.69Chapter 6 --- Conclusions --- p.70Chapter 6.1 --- Future Work --- p.72Bibliography --- p.7

Non-parametric linear time-invariant system identification by discrete wavelet transforms

We describe the use of the discrete wavelet transform (DWT) for non-parametric linear time-invariant system identification. Identification is achieved by using a test excitation to the system under test (SUT) that also acts as the analyzing function for the DWT of the SUT's output, so as to recover the impulse response. The method uses as excitation any signal that gives an orthogonal inner product in the DWT at some step size (that cannot be 1). We favor wavelet scaling coefficients as excitations, with a step size of 2. However, the system impulse or frequency response can then only be estimated at half the available number of points of the sampled output sequence, introducing a multirate problem that means we have to 'oversample' the SUT output. The method has several advantages over existing techniques, e.g., it uses a simple, easy to generate excitation, and avoids the singularity problems and the (unbounded) accumulation of round-off errors that can occur with standard techniques. In extensive simulations, identification of a variety of finite and infinite impulse response systems is shown to be considerably better than with conventional system identification methods.Department of Computin

On designing H∞ filters with circular pole and error variance constraints

Copyright [2003] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, we deal with the problem of designing a H∞ filter for discrete-time systems subject to error variance and circular pole constraints. Specifically, we aim to design a filter such that the H∞ norm of the filtering error-transfer function is not less than a given upper bound, while the poles of the filtering matrix are assigned within a prespecified circular region, and the steady-state error variance for each state is not more than the individual prespecified value. The filter design problem is formulated as an auxiliary matrix assignment problem. Both the existence condition and the explicit expression of the desired filters are then derived by using an algebraic matrix inequality approach. The proposed design algorithm is illustrated by a numerical example