This thesis presents a study on the design of two-dimensional (2-D) digital filters by using the singular-value decomposition (SVD). A new method for the design of 2-D quadrantally symmetric FIR filters with linear phase response is proposed. It is shown that three realizations are possible, namely, a direct realization, a modified version of the direct realization, and a realization based on the combined application of the SV and LU decompositions. Each of the three realizations consists of a parallel arrangement of cascaded pairs of 1-D filters; hence extensive parallel processing and pipelining can be applied. The three realizations are compared and it is shown that the realization based on the SV and LU decomposition leads to the lowest approximation error and involves the smallest number of multiplications. It is shown that the SVD of the sampled amplitude response of a 2-D digital filter with real coefficients possesses a special structure: every singular vector is either mirror-image symmetric or antisymmetric with respect to its midpoint. Consequently, the SVD method can be applied along with 1-D FIR techniques for the design of linear-phase 2-D filters with arbitrary prescribed amplitude responses which are symmetrical with respect to the origin of the (ω1, ω2) plane. A method for the design of 2-D IIR digital filters based on the combined application of the SVD and the balanced approximation (BA) is proposed. It is shown that the approximation error in the phase angle is bounded by the sum of the neglected Hankel singular values of the filter. Consequently, the phase response of the resulting filter is approximately linear over the passband region provided that only small Hankel singular values are neglected. It is also shown that the resulting 2-D filter is nearly balanced, which implies that the filter has low roundoff noise as well as low parameter sensitivity. Furthermore, the 2-D filter obtained is more economical and computationally more efficient than the original 2-D FIR filter, and in the case where an IIR filter is obtained the stability of the filter is guaranteed. Efficient general algorithms for the evaluation of the 1-D and 2-D gramians for 1-D and 2-D, causal, stable, recursive digital filters are proposed, which facilitate the application of the BA method in the design of digital filters. The algorithms obtained are based on a two-stage extension of the Astrom-Jury-Agniel (AJA) algorithm. It is shown that the AJA algorithm can be modified to solve a 1-D Lyapunov equation in a recursive manner. The recursive algorithm is then extended to the case where the rational function vector involved depends on two complex variables. It is shown that the two algorithms obtained can be combined to evaluate the 2-D gramians. The proposed algorithms are also useful in obtaining optimal digital filter structures that minimize the output-noise power due to the roundoff of products. / Graduate

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by Lai Wai Kuen. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1993. / Includes bibliographical references (leaves [119-125]). / Abstract --- p.i / Acknowledgement --- p.ii / Table of Contents --- p.iii / Chapter Chapter 1 --- Introduction / Chapter 1.1 --- Background - The Need for Nonlinear Filtering --- p.1.1 / Chapter 1.2 --- Nonlinear Filtering --- p.1.2 / Chapter 1.3 --- Goal of the Work --- p.1.4 / Chapter 1.4 --- Organization of the Thesis --- p.1.5 / Chapter Chapter 2 --- An Overview of Robust Estimator Based Filters Morphological Filters / Chapter 2.1 --- Introduction --- p.2.1 / Chapter 2.2 --- Signal Representation by Sets --- p.2.2 / Chapter 2.3 --- Robust Estimator Based Filters --- p.2.4 / Chapter 2.3.1 --- Filters based on the L-estimators --- p.2.4 / Chapter 2.3.1.1 --- The Median Filter and its Derivations --- p.2.5 / Chapter 2.3.1.2 --- Rank Order Filters and Derivations --- p.2.9 / Chapter 2.3.2 --- Filters based on the M-estimators (M-Filters) --- p.2.11 / Chapter 2.3.3 --- Filter based on the R-estimators --- p.2.13 / Chapter 2.4 --- Filters based on Mathematical Morphology --- p.2.14 / Chapter 2.4.1 --- Basic Morphological Operators --- p.2.14 / Chapter 2.4.2 --- Morphological Filters --- p.2.18 / Chapter 2.5 --- Chapter Summary --- p.2.20 / Chapter Chapter 3 --- Multi-Structuring Element Erosion Filter / Chapter 3.1 --- Introduction --- p.3.1 / Chapter 3.2 --- Problem Formulation --- p.3.1 / Chapter 3.3 --- Description of Multi-Structuring Element Erosion Filter --- p.3.3 / Chapter 3.3.1 --- Definition of Structuring Element for Multi-Structuring Element Erosion Filter --- p.3.4 / Chapter 3.3.2 --- Binary multi-Structuring Element Erosion Filter --- p.3.9 / Chapter 3.3.3 --- Selective Threshold Decomposition --- p.3.10 / Chapter 3.3.4 --- Multilevel Multi-Structuring Element Erosion Filter --- p.3.15 / Chapter 3.3.5 --- A Combination of Multilevel Multi-Structuring Element Erosion Filter and its Dual --- p.3.21 / Chapter 3.4 --- Chapter Summary --- p.3.21 / Chapter Chapter 4 --- Properties of Multi-Structuring Element Erosion Filter / Chapter 4.1 --- Introduction --- p.4.1 / Chapter 4.2 --- Deterministic Properties --- p.4.2 / Chapter 4.2.1 --- Shape of Invariant Signal --- p.4.3 / Chapter 4.2.1.1 --- Binary Multi-Structuring Element Erosion Filter --- p.4.5 / Chapter 4.2.1.2 --- Multilevel Multi-Structuring Element Erosion Filter --- p.4.16 / Chapter 4.2.2 --- Rate of Convergence of Multi-Structuring Element Erosion Filter --- p.4.25 / Chapter 4.2.2.1 --- Convergent Rate of Binary Multi-Structuring Element Erosion Filter --- p.4.25 / Chapter 4.2.2.2 --- Convergent Rate of Multilevel Multi-Structuring Element Erosion Filter --- p.4.28 / Chapter 4.3 --- Statistical Properties --- p.4.30 / Chapter 4.3.1 --- Output Distribution of Multi-Structuring Element Erosion Filter --- p.4.30 / Chapter 4.3.1.1 --- One-Dimensional Statistical Analysis of Multilevel Multi-Structuring Element Erosion Filter --- p.4.31 / Chapter 4.3.1.2 --- Two-Dimensional Statistical Analysis of Multilevel Multi-Structuring Element Erosion Filter --- p.4.32 / Chapter 4.3.2 --- Discussions on Statistical Properties --- p.4.36 / Chapter 4.4 --- Chapter Summary --- p.4.40 / Chapter Chapter 5 --- Performance Evaluation / Chapter 5.1 --- Introduction --- p.5.1 / Chapter 5.2 --- Performance Criteria --- p.5.2 / Chapter 5.2.1 --- Noise Suppression --- p.5.5 / Chapter 5.2.2 --- Subjective Criterion --- p.5.16 / Chapter 5.2.3 --- Computational Requirement --- p.5.20 / Chapter 5.3 --- Chapter Summary --- p.5.23 / Chapter Chapter 6 --- Recapitulation and Suggestions for Further Work / Chapter 6.1 --- Recapitulation --- p.6.1 / Chapter 6.2 --- Suggestions for Further Work --- p.6.4 / Chapter 6.2.1 --- Probability Measure Function for the Two-Dimensional Filter --- p.6.4 / Chapter 6.2.2 --- Hardware Implementation --- p.6.5 / References / Appendices

by Ma Wing-Kin. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references (leaves 121-124). / Chapter 1 --- Introduction to Otoacoustic Emissions --- p.1 / Chapter 1.1 --- Introduction --- p.1 / Chapter 1.2 --- Clinical Significance of the OAEs --- p.2 / Chapter 1.3 --- Classes of OAEs --- p.3 / Chapter 1.4 --- The Distortion Product OAEs --- p.4 / Chapter 1.4.1 --- Measurement of DPOAEs --- p.5 / Chapter 1.4.2 --- Some Properties of DPOAEs --- p.8 / Chapter 1.4.3 --- Noise Reduction of DPOAEs --- p.8 / Chapter 1.5 --- Goal of this work and Organization of the Thesis --- p.9 / Chapter 2 --- Review to some Topics in Narrowband Signal Estimation --- p.11 / Chapter 2.1 --- Fourier Transforms --- p.12 / Chapter 2.2 --- Periodogram ´ؤ Classical Spectrum Estimation Method --- p.15 / Chapter 2.2.1 --- Signal-to-Noise Ratios and Equivalent Noise Bandwidth --- p.17 / Chapter 2.2.2 --- Scalloping --- p.18 / Chapter 2.3 --- Maximum Likelihood Estimation --- p.19 / Chapter 2.3.1 --- Finding of the ML Estimator --- p.19 / Chapter 2.3.2 --- Properties of the ML Estimator --- p.21 / Chapter 3 --- Review to Adaptive Notch/Bandpass Filter --- p.23 / Chapter 3.1 --- Introduction --- p.23 / Chapter 3.2 --- Filter Structure --- p.24 / Chapter 3.3 --- Adaptation Algorithms --- p.25 / Chapter 3.3.1 --- Least Squares Method --- p.25 / Chapter 3.3.2 --- Least-Mean-Squares Algorithm --- p.27 / Chapter 3.3.3 --- Recursive-Least-Squares Algorithm --- p.28 / Chapter 3.4 --- LMS ANBF Versus RLS ANBF --- p.31 / Chapter 3.5 --- the IIR filter Versus ANBF --- p.31 / Chapter 4 --- Fast RLS Adaptive Notch/Bandpass Filter --- p.33 / Chapter 4.1 --- Motivation --- p.33 / Chapter 4.2 --- Theoretical Analysis of Sample Autocorrelation Matrix --- p.34 / Chapter 4.2.1 --- Solution of Φ (n) --- p.34 / Chapter 4.2.2 --- Approximation of Φ (n) --- p.35 / Chapter 4.3 --- Fast RLS ANBF Algorithm --- p.37 / Chapter 4.4 --- Performance Study --- p.39 / Chapter 4.4.1 --- Relationship to LMS ANBF and Bandwidth Evaluation . --- p.39 / Chapter 4.4.2 --- Estimation Error of Tap Weights --- p.40 / Chapter 4.4.3 --- Residual Noise Power of Bandpass Output --- p.42 / Chapter 4.5 --- Simulation Examples --- p.43 / Chapter 4.5.1 --- Estimation of Single Sinusoid in Gaussian White Noise . --- p.43 / Chapter 4.5.2 --- Comparing the Performance of IIR Filter and ANBFs . . --- p.44 / Chapter 4.5.3 --- Harmonic Signal Enhancement --- p.45 / Chapter 4.5.4 --- Cancelling 50/60Hz Interference in ECG signal --- p.46 / Chapter 4.6 --- Simulation Results of Performance Study --- p.52 / Chapter 4.6.1 --- Bandwidth --- p.52 / Chapter 4.6.2 --- Estimation Errors --- p.53 / Chapter 4.7 --- Concluding Summary --- p.55 / Chapter 4.8 --- Appendix A: Derivation of Ts --- p.56 / Chapter 4.9 --- Appendix B: Derivation of XT(n)Λ(n)ΛT(n)X(n) --- p.56 / Chapter 5 --- Investigation of the Performance of two Conventional DPOAE Estimation Methods --- p.58 / Chapter 5.1 --- Motivation --- p.58 / Chapter 5.2 --- The DPOAE Signal Model --- p.59 / Chapter 5.3 --- Preliminaries to the Conventional Methods --- p.60 / Chapter 5.3.1 --- Conventional Method 1: Constrained Stimulus Generation --- p.60 / Chapter 5.3.2 --- Conventional Method 2: Windowing --- p.61 / Chapter 5.4 --- Performance Comparison --- p.63 / Chapter 5.4.1 --- Sidelobe Level Reduction --- p.63 / Chapter 5.4.2 --- Estimation Accuracy --- p.65 / Chapter 5.4.3 --- Noise Floor Level --- p.67 / Chapter 5.4.4 --- Additional Loss by Scalloping --- p.68 / Chapter 5.5 --- Simulation Study --- p.69 / Chapter 5.5.1 --- Sidelobe Suppressions of the Windows --- p.69 / Chapter 5.5.2 --- Mean Level Estimation --- p.70 / Chapter 5.5.3 --- Mean Squared Error Analysis --- p.71 / Chapter 5.6 --- Concluding Summary --- p.75 / Chapter 5.7 --- Discussion --- p.75 / Chapter 5.8 --- Appendix A: Cramer-Rao Bound of the DPOAE Level Estimation --- p.76 / Chapter 6 --- Theoretical Considerations of Maximum Likelihood Estimation for the DPOAEs --- p.77 / Chapter 6.1 --- Motivation --- p.77 / Chapter 6.2 --- Finding of the MLEs --- p.78 / Chapter 6.2.1 --- First Form: Joint Estimation of DPOAE and Artifact Pa- rameter --- p.79 / Chapter 6.2.2 --- Second Form: Artifact Cancellation --- p.80 / Chapter 6.3 --- Relationship of CM1 to MLE --- p.81 / Chapter 6.4 --- Approximating the MLE --- p.82 / Chapter 6.5 --- Concluding Summary --- p.84 / Chapter 6.6 --- Appendix A: Equivalent Forms for the Minimum Least Squares Error --- p.85 / Chapter 7 --- Optimum Estimator Structure and Artifact Cancellation Ap- proaches for the DPOAEs --- p.87 / Chapter 7.1 --- Motivation --- p.87 / Chapter 7.2 --- The Optimum Estimator Structure --- p.88 / Chapter 7.3 --- References and Frequency Offset Effect --- p.89 / Chapter 7.4 --- Artifact Canceling Algorithms --- p.92 / Chapter 7.4.1 --- Least-Squares Canceler --- p.93 / Chapter 7.4.2 --- Windowed-Fourier-Transform Canceler --- p.93 / Chapter 7.4.3 --- FRLS Adaptive Canceler --- p.95 / Chapter 7.5 --- Time-domain Noise Rejection --- p.97 / Chapter 7.6 --- Regional Periodogram --- p.98 / Chapter 7.7 --- Experimental Results --- p.99 / Chapter 7.7.1 --- Artifact Cancellation via External Reference --- p.99 / Chapter 7.7.2 --- Artifact Cancellation via Internal Reference --- p.99 / Chapter 7.7.3 --- Artifact Cancellation in presence of Transient Noise --- p.101 / Chapter 7.7.4 --- Illustrative Example: DPgrams --- p.102 / Chapter 7.8 --- Conclusion and Discussion --- p.111 / Chapter 7.9 --- Appendix A: Derivation of the Parabolic Interpolation Method . --- p.113 / Chapter 7.10 --- Appendix B: Derivation of Weighted-Least-Squares Canceler . . --- p.114 / Chapter 8 --- Conclusions and Future Research Directions --- p.118 / Chapter 8.1 --- Conclusions --- p.118 / Chapter 8.2 --- Future Research Directions --- p.119 / Bibliography --- p.121

Graduation date: 1995

A new circuit technique called Folded Source Coupled Logic (FSCL) has been developed to implement the digital section of mixed-signal IC applications. This FSCL circuit technique offers the advantage of low overlap current spikes during the switching transitions of conventional CMOS gates. This overlap current spike has become one of the major obstacles in improving the accuracy and performance of mixed-signal IC applications. Using simple circuits, FSCL logic family can be interfaced with the existing CMOS family. Thus it can nearly eliminate the power noise issue in the mixed-signal IC design. In this thesis, design of a sinc3 decimation filter using the FSCL technique for a 2nd order delta-sigma modulator has been presented. Simulation results show that this particular decimation filter, using the newly developed FSCL technique, improves the performance of the mixed-signal system. / Graduation date: 1994

Thesis (M.S.)--State University of New York at Binghamton, Thomas J. Watson School of Engineering and Applied Science, Department of Electrical and Computer Engineering, 2009. / Includes bibliographical references.

published_or_final_version / abstract / toc / Electrical and Electronic Engineering / Master / Master of Philosophy

Subband/Wavelet filter analysis-synthesis filters are a major component in many compression algorithms. Such compression algorithms have been applied to images, voice, and video. These algorithms have achieved high performance. Typically, the configuration for such compression algorithms involves a bank of analysis filters whose coefficients have been designed in advance to enable high quality reconstruction. The analysis system is then followed by subband quantization and decoding on the synthesis side. Decoding is performed using a corresponding set of synthesis filters and the subbands are merged together. For many years, there has been interest in improving the analysis-synthesis filters in order to achieve better coding quality. Adaptive filter banks have been explored by a number of authors where by the analysis filters and synthesis filters coefficients are changed dynamically in response to the input. A degree of performance improvement has been reported but this approach does require that the analysis system dynamically maintain synchronization with the synthesis system in order to perform reconstruction. In this thesis, we explore a variant of the adaptive filter bank idea. We will refer to this approach as fixed-analysis adaptive-synthesis filter banks. Unlike the adaptive filter banks proposed previously, there is no analysis synthesis synchronization issue involved. This implies less coder complexity and more coder flexibility. Such an approach can be compatible with existing subband wavelet encoders. The design methodology and a performance analysis are presented.

Thesis(M. Tech.) - Central University of Technology, Free State, 2004 / Growing markets leads to an increase in production. In these modern industries, weight measurement is of high priority. Weight measurement instrumentation is used for quality control, as well as for effective process control. Ineffective instrumentation with inaccurate data will influence the production process and profit margins negatively. Experimental data is gathered from an angled load cell, placed as a crossover between two conveyer belts. A weight measurement instrument with the ability to acquire accurate measurement of individual, moving parts is produced with the aid of DSP techniques. This was accomplished by analyzing the frequency spectrum for the undesirable signals with the use of Wavelets transformations (WT) and Fourier transformations (FT). After these undesired signals were identified a digital filter was designed to remove the undesired signals. Repetition of performance is achieved by the automatic zeroing of the instrument after every individual measurement. This weight measurement instrumentation also has the ability to store data consisting of the amount of objects and their individual weights. This instrument can also determine the material of which an object is made of. This is done by calculating the friction coefficient. This function has the ability to effectively identify between iron and rubber components irrespective of their mass or area.