Adaptive System Identication Based on All Pass/Minimum Phase System Decomposition 1
In this paper we present a novel adaptive IIR digital lter composed of a cascade of an all-pass lter and a minimum- phase lter. The coecien ts of the lter are updated in such a way as to achieve minimum mean-squared error between the output of the unknown system and the output of the digital lter. Computer simulation veries that the digital lter coecien ts converge to the unknown system coecien ts in the case where the system is com- posed of a cascade of all-pass section and minimum phase section. Keywords | system identication, adaptive lters.
An adaptive IIR digital filter based on estimation of allpass and minimum-phase system
In this paper, a new infinite impulse response (IIR) adaptive digital filter (ADF) which is composed of a cascade block of allpass system and a block of minimum-phase system connected in series is proposed. The allpass section is implemented using a series connection of second order allpass systems, while the minimum phase system has all its poles at the origin. The coefficients are updated using a simplified version of the LMS algorithm. By considering the unknown system to be having the same structure as that of the adaptive digital filter, it is proven that the poles of the ADF converges to the poles of the unknown system when the input is a stationary white signal. Computer simulation confirms our analysis.
Analog and Digital Signal Processing
LIST OF TABLES / PREFACE / FROM THE PREFACE TO THE FIRST EDITION 1. OVERVIEW Introduction / Signals / Systems / The Frequency Domain / From Concept to Application 2. ANALOG SIGNALS Scope and Objectives / Signals / Operations on Signals / Signal Symmetry / Harmonic Signals and Sinusoids / Signal Symmetry / Harmonic Signals and Sinusoids / Commonly Encountered Signals / The Impulse Function / The Doublet / Moments / Problems 3. DISCRETE SIGNALS Scope and Objectives / Discrete Signals / Operations on Discrete Signals / Decimation and Interpolation / Common Discrete Signals / Discrete-Time Harmonics and Sinusoids / Aliasing and the Sampling Theorem / Random Signals / Problems 4. ANALOG SYSTEMS Scope and Objectives / Introduction / System Classification / Analysis of LTI Systems / LTI Systems Described by Differential Equations / The Impulse Response of LTI Systems / System Stability / Application-Oriented Examples / Problems 5. DISCRETE-TIME SYSTEMS Scope and Objectives / Discrete-Time Operators / System Classification / Digital Filters / Digital Filters Described by Difference Equations / Impulse Response of Digital Filters / Stability of Discrete-Time LTI Systems / Connections: System Representation in Various Forms / Application-Oriented Examples / Problems 6. CONTINUOUS CONVOLUTION Scope and Objectives / Introduction / Convolution of Some Common Signals / Some Properties of Convolution / Convolution by Ranges (Graphical Convolution) / Stability and Causality / The Response to Periodic Inputs / Periodic Convolution / Connections: Convolution and Transform Methods / Convolution Properties Based on Moments / Correlations / Problems 7. DISCRETE CONVOLUTION Scope and Objectives / Discrete Convolution / Convolution Properties / Convolution of Finite Sequences / Stability and Causality of LTI Systems / System Response to Periodic Inputs / Periodic Convolution / Connections: Discrete Convolution and Transform Methods / Deconvolution / Discrete Correlation / Problems 8. FOURIER SERIES Scope and Objectives / Fourier Series: A First Look / Simplifications Through Signal Symmetry / Parseval"s Relation and the Power in Periodic Signals / The Spectrum of Periodic Signals / Properties of Fourier Series / Signal Reconstruction and the Gibbs Effect / System Response to Periodic Inputs / Application-Oriented Examples / The Dirichlet Kernel and the Gibbs Effect / The Fourier Series, Orthogonality, and Least Squares / Existence, Convergence, and Uniqueness / A Historical Perspective / Problems 9. THE FOURIER TRANSFORM Scope and Objectives / Introduction / Fourier Transform Pairs and Properties / System Analysis Using the Fourier Transform / Frequency Response of Filters / Energy and Power Spectral Density / Time-Bandwidth Measures / Problems 10. MODULATION Scope and Objectives / Amplitude Modulation / Single-Sideband AM / Angle Modulation / Wideband Angle Modulation / Demodulation of FM Signals / The Hilbert Transform / Problems 11. THE LAPLACE TRANSFORM Scope and Objectives / The Laplace Transform / Properties of the Laplace Transform / Poles and Zeros of the Transfer Function / The Inverse Laplace Transform / The s-plane and BIBO Stability / The Laplace Transform and System Analysis / Connections / Problems 12. APPLICATIONS OF THE LAPLACE TRANSFORM Scope and Objectives / Frequency Response / Minimum-Phase Filters / Bode Plots / Performance Measures / Feedback / Application of Feedback: The Phase-Locked Loop Problems 13. ANALOG FILTERS Scope and Objectives / Introduction / The Design Process / The Butterworth Filter / The Chebyshev Approximation / The Inverse Chebyshev Approximation / The Elliptic Approximation / The Bessel Approximation / Problems 14. SAMPLING AND QUANTIZATION Scope and Objectives / Ideal Sampling / Sampling, Interpolation, and Signal Recovery / Quantization / Digital Processing of Analog Signals / Compact Disc Digital Audio / Dynamic Range Processors / Problems 15. THE DISCRETE-TIME FOURIER TRANSFORM Scope and Objectives / The Discrete-Time Fourier Transform / Connections: The DTFT and the Fourier Transform / Properties of the DTFT / The Transfer Functions / System Analysis Using the DTFT / Connections / Ideal Filters / Some Traditional and Non-traditional Filters / Frequency Response of Discrete Algorithms / Oversampling and Sampling Rate Conversion / Problems 16. THE DFT AND FFT Scope and Objectives / Introduction / Properties of the DFT / Connections / Approximating the DTFT by the DFT / The DFT of Periodic Signals / Spectral Smoothing by Time Windows / Applications in Signal Processing / Spectrum Estimation / Matrix Formulation of the DFT and IDFT / The FFT / Why Equal Lengths for the DFT and IDFT? / Problems 17. THE Z-TRANSFORM Scope and Objectives / The Two-Sided z-Transform / Properties of the z-Transform / Poles, Zeros, and the z-Plane / The Transfer Function / The Inverse z-Transform / The One-Sided z-Transform / The z-Transform and System Analysis / Frequency Response / Connections / Problems 18. APPLICATIONS OF THE Z-TRANSFORM Scope and Objectives / Transfer Function Realization / Interconnected Systems / Minimum-Phase Systems / The Frequency Response: A Graphical Interpretation / Application-Oriented Examples / Allpass Filters / Application-Oriented Examples: Digital Audio Effects / Problems 19. IIR DIGITAL FILTERS Scope and Objectives / Introduction / IIR Filter Design / Response and Matching / The Matched z-Transform for Factored Forms / Mappings from Discrete Algorithms / The Bilinear Transformation / Spectral Transformations for IIR Filters / Design Recipe for IIR Filters / Problems 20. FIR DIGITAL FILTERS Scope and Objectives / Symmetric Sequences and Linear Phase / Window-Based Design / Half-Band FIR Filters / FIR Filter Design by Frequency Sampling / Design of Optimal Linear-Phase FIR Filters / Application: Multistage Interpolation and Decimation / Maximally Flat FIR Filters / FIR Differentiators and Hilbert Transformers / Least Squares and Adaptive Signal Processing / Problems 21. MATLAB(R) EXAMPLES Introduction / ADSP Toolbox and Its Installation / MATLAB Tips and Pointers / Graphical User Interface Programs / The ADSP Toolbox / Examples of MATLAB Code / REFERENCES / INDEX