Optimal cosine modulated nonuniform linear phase FIR filter bank design via stretching and shifting frequency response of prototype filter

This paper proposes an optimal cosine modulated nonuniform linear phase finite impulse response (FIR) filter bank design. The frequency responses of all the analysis filters and the synthesis filters of the filter bank are derived based on both stretching and shifting the frequency response of the prototype filter. The total aliasing error of the filter bank is minimized subject to a specification on the maximum amplitude distortion of the filter bank as well as specifications on both the maximum passband ripple magnitude and the maximum stopband ripple magnitude of the prototype filter. This filter bank design problem is actually a functional inequality constrained optimization problem. Our recently developed integration approach is employed for solving the problem. Computer numerical simulation results show that our proposed design method outperforms existing design methods

Quarterly Research Output Reports

These reports paper summarize research outputs published in each quarter by academic staff at the University of Lincoln. The lists include substantive research outputs first appearing "in published form" (or equivalent for non-textual outputs) during this period. The lists have been generated automatically from data stored in the Lincoln Repository (http://eprints.lincoln.ac.uk/). Tables summarize the volume of outputs recorded by School

Wavelets and Subband Coding

First published in 1995, Wavelets and Subband Coding offered a unified view of the exciting field of wavelets and their discrete-time cousins, filter banks, or subband coding. The book developed the theory in both continuous and discrete time, and presented important applications. During the past decade, it filled a useful need in explaining a new view of signal processing based on flexible time-frequency analysis and its applications. Since 2007, the authors now retain the copyright and allow open access to the book

Optimal Design of Cosine Modulated Nonuniform Linear Phase FIR Filter Bank via Both Stretching and Shifting Frequency Response of Single Prototype Filter

This paper designs an optimal cosine modulated nonuniform linear phase finite impulse response (FIR) filter bank. The frequency responses of all the analysis filters and the synthesis filters of the filter bank are derived based on both stretching and shifting the frequency response of a single prototype filter. The total aliasing error of the filter bank is minimized subject to specifications on the maximum magnitude distortion of the filter bank and the maximum ripple magnitudes of the prototype filter over both the passband and the stopband. This paper proposes a joint constraint transcription and modified filled function method for solving the optimization problem. In particular, the functional inequality constraints are converted to discrete constraints via the constraint transcription method. The globally optimal solution of the nonconvex optimization problem can be found efficiently via the modified filled function method. Computer numerical simulation results show that our design outperforms existing designs

Analysis of Nonlinear Behaviors, Design and Control of Sigma Delta Modulators

M PhilSigma delta modulators (SDMs) have been widely applied in analogue-to-digital (A/D) conversion for many years. SDMs are becoming more and more popular in power electronic circuits because it can be viewed and applied as oversampled A/D converters with low resolution quantizers. The basic structure of an SDM under analytical investigation consists of a loop filter and a low bit quantizer connected by a negative feedback loop. Although there are numerous advantages of SDMs over other A/D converters, the application of SDMs is limited by the unboundedness of the system states and their nonlinear behaviors. It was found that complex dynamical behaviors exist in low bit SDMs, and for a bandpass SDM, the state space dynamics can be represented by elliptic fractal patterns confined within two trapezoidal regions. In all, there are three types of nonlinear behaviors, namely fixed point, limit cycle and chaotic behaviors. Related to the unboundedness issue, divergent behavior of system states is also a commonly discovered phenomenon. Consequently, how to design and control the SDM so that the system states are bounded and the unwanted nonlinear behaviors are avoided is a hot research topic worthy of investigated. In our investigation, we perform analysis on such complex behaviors and determine a control strategy to maintain the boundedness of the system states and avoid the occurrence of limit cycle behavior. For the design problem, we impose constraints based on the performance of an SDM and determine an optimal design for the SDM. The results are significantly better than the existing approaches

Ambisonics

This open access book provides a concise explanation of the fundamentals and background of the surround sound recording and playback technology Ambisonics. It equips readers with the psychoacoustical, signal processing, acoustical, and mathematical knowledge needed to understand the inner workings of modern processing utilities, special equipment for recording, manipulation, and reproduction in the higher-order Ambisonic format. The book comes with various practical examples based on free software tools and open scientific data for reproducible research. The book’s introductory section offers a perspective on Ambisonics spanning from the origins of coincident recordings in the 1930s to the Ambisonic concepts of the 1970s, as well as classical ways of applying Ambisonics in first-order coincident sound scene recording and reproduction that have been practiced since the 1980s. As, from time to time, the underlying mathematics become quite involved, but should be comprehensive without sacrificing readability, the book includes an extensive mathematical appendix. The book offers readers a deeper understanding of Ambisonic technologies, and will especially benefit scientists, audio-system and audio-recording engineers. In the advanced sections of the book, fundamentals and modern techniques as higher-order Ambisonic decoding, 3D audio effects, and higher-order recording are explained. Those techniques are shown to be suitable to supply audience areas ranging from studio-sized to hundreds of listeners, or headphone-based playback, regardless whether it is live, interactive, or studio-produced 3D audio material

Wavelet Theory

The wavelet is a powerful mathematical tool that plays an important role in science and technology. This book looks at some of the most creative and popular applications of wavelets including biomedical signal processing, image processing, communication signal processing, Internet of Things (IoT), acoustical signal processing, financial market data analysis, energy and power management, and COVID-19 pandemic measurements and calculations. The editor’s personal interest is the application of wavelet transform to identify time domain changes on signals and corresponding frequency components and in improving power amplifier behavior

Doppler Encoded Excitation Patterning (DEEP) Microscopy

Traditional optical imaging systems rely on lenses and spatially-resolved detection to probe distinct locations on the object. We develop a novel computational approach to 2D and 3D imaging that instead measures the object\u27s spatial Fourier transform using a single-element detector and without requiring precision optics. This wide-field technique can be used to image biological and synthetic structures in fluoresced or scattered light using coherent or broadband illumination. It employs dynamic structured illumination, acousto-optics, RF electronics, and tomographic algorithms to circumvent several trade-offs in conventional imaging, such as the dependence of the optical transfer function on the imaging lenses and the coupling of resolution and depth of field. We use Fourier optics concepts to derive the dynamic optical transfer function, evaluate different Fourier sampling strategies, and investigate and compare tomographic algorithms for 2D and 3D image synthesis. We also develop conceptual and analytical models to describe imaging of fluorescent as well as amplitude and phase scattering objects, the effects of broadband and spatially-incoherent illumination, and nonlinear wide-field super-resolution imaging. We consider sources of noise, analyze and simulate SNR behavior for several types of noise and Fourier sampling strategies, and compare the sensitivity of the technique to conventional imaging. We describe several experimental proof-of-concept systems and present two-dimensional high-resolution tomographic image reconstructions in both scattered and fluoresced light demonstrating a thousandfold improvement in the depth of field compared to conventional lens-based microscopy. Finally, we explore approaches for high-speed Fourier sampling and propose several related sensing techniques, including wide-field fluorescence imaging in scattering media