In Chapter 1, using the differential equation as the fundamental system description, we show how to obtain the filtering functions associated with physical systems; namely, the impulse response, step response, weighting function, and convolution integral. Chapter 2 introduces the Fourier and Laplace transforms, which lead to the frequency-domain system descriptions including the transfer function, magnitude response, phase response, and group-delay response. An introduction to the Hilbert transform, which is useful for relating specific network functions. In chapter 3 theoretical and realizable lowpass responses, including limitations in the time and frequency domains, are discussed. In Chapter 4 we concentrate on the transformation of the normalized lowpass prototype into other filter types. The narrowband and bandpass filter is discussed in detail because its analysis is applicable to crystal, helical, coaxial cavity, stripline, interdigital, and waveguide filters. In chapter 5 we consider the all-pass function, a function that is useful for phase and group delay equalization and for the simulation of specified delay. In chapter 6 we discuss the finite Q elements and predistortion. In chapter 7 we switch the focus from classical filter treatment to a consideration of the filtering of signals in a noisy environment, in particular, the matched filter. In chapter 8 we discuss the two methods of time-domain synthesis, the quasi-stationary approach to the analysis of linear systems excited by modulated inputs, and the subject of average time delay. Chapter 9 is devoted to digital filtering and includes a discussion of the z-transform
A digital filter can be pictured as a "black box" that accepts a sequence of numbers and emits a new sequence of numbers. In digital audio signal processing applications, such number sequences usually represent sounds. For example, digital filters are used to implement graphic equalizers and other digital audio effects. This book is a gentle introduction to digital filters, including mathematical theory, illustrative examples, some audio applications, and useful software starting points. The theory treatment begins at the high-school level, and covers fundamental concepts in linear systems theory and digital filter analysis. Various "small" digital filters are analyzed as examples, particularly those commonly used in audio applications. Matlab programming examples are emphasized for illustrating the use and development of digital filters in practice.
This open access book comprehensively covers the fundamentals of clinical data science, focusing on data collection, modelling and clinical applications. Topics covered in the first section on data collection include: data sources, data at scale (big data), data stewardship (FAIR data) and related privacy concerns. Aspects of predictive modelling using techniques such as classification, regression or clustering, and prediction model validation will be covered in the second section. The third section covers aspects of (mobile) clinical decision support systems, operational excellence and value-based healthcare. Fundamentals of Clinical Data Science is an essential resource for healthcare professionals and IT consultants intending to develop and refine their skills in personalized medicine, using solutions based on large datasets from electronic health records or telemonitoring programmes. The book’s promise is “no math, no code”and will explain the topics in a style that is optimized for a healthcare audience.
The text focuses on the creation, manipulation, transmission, and reception of information by electronic means. Contents: 1) Introduction. 2) Signals and Systems. 3) Analog Signal Processing. 4) Frequency Domain. 5) Digital Signal Processing. 6) Information Communication. 7) Appendices: Decibels; Permutations and Combinations, Frequency Allocations.
Offers a well-rounded, mathematical approach to problems in signal interpretation using the latest time, frequency, and mixed-domain methods Equally useful as a reference, an up-to-date review, a learning tool, and a resource for signal analysis techniques Provides a gradual introduction to the mathematics so that the less mathematically adept reader will not be overwhelmed with instant hard analysis Covers Hilbert spaces, complex analysis, distributions, random signals, analog Fourier transforms, and more
Complexity reduction is one of the main issues of digital signal processing (DSP) algorithms, especially in communication systems where each new generation brings new requirements towards increasing data rates and improved accuracy positioning, leading to the growth of power consumption and chip area. To meet these requirements and at the same time find a trade-off between high performance and low implementation cost, more sophisticated DSP algorithms need to be developed. Recent communication standards require flexible, adaptive systems capable of real-time frequency-domain tuning. Variable digital filters (VDFs) address these needs by enabling "on-the-fly" frequency response adjustments without the need for online filter design. The key feature of VDFs is that they require only an adjustment of one or a few parameters to change their characteristics, without the need for extensive additional computations. Most VDF coefficients remain fixed after the initial design, allowing for efficient hardware implementation. This makes VDFs essential for modern adaptive communication technologies. This thesis primarily focuses on the design and low-complexity implementation techniques of VDFs and presents three main contributions. Firstly, it proposes three VDF realizations for simultaneous lowpass filtering and equalization using polynomial channel models, with systematic design procedures based on minimax optimization for all the proposed structures. In addition, a fast design method for the VDFs with several variable parameters, which can substantially decrease the design time, is presented. Secondly, it introduces frequency-domain implementations of VDFs using the overlap-save technique. Based on the assumption that these filters have been designed using a common design approach based on optimizing the impulse response coefficients, the filter DFT coefficients are proposed to be implemented as fixed, hybrid, or variable weights. Lastly, the thesis presents an efficient design approach for a variable-bandwidth digital filter implemented in the frequency domain using the overlap-save method. The proposed approach is based on a hybrid of frequency sampling and optimization, allowing for direct optimization of the DFT coefficients considering the filter frequency-domain implementation and thereby noticeably reducing the cost of implementation and an online update of the DFT filter coefficients when the bandwidth is varied. Reduktion av komplexitet är en av huvudfrågorna för digital signalbehandling (DSP) algoritmer, särskilt i kommunikationssystem där varje ny generation ställer nya krav på att öka datahastigheter och förbättrad noggrannhet positionering, vilket leder till en ökning av strömförbrukningen och kretsytan. För att möta dessa krav och samtidigt hitta en avvägning mellan hög prestanda och låg implementeringskostnad behöver mer sofistikerade DSP-algoritmer utvecklas. Senaste kommunikationsstandarder kräver flexibla, adaptiva system som kan frekvensdomäninställning i realtid. Variabla digitala filter (VDF) tillgodoser dessa behov genom att möjliggöra "on-the-fly" frekvenssvarsjusteringar utan behov av onlinefilterdesign. Nyckelegenskapen hos VDF:er är att de bara kräver en justering av en eller ett fåtal parametrar för att ändra deras egenskaper, utan behov av omfattande ytterligare beräkningar. De flesta VDF-koefficienter förblir fixerade efter den ursprungliga designen, vilket möjliggör effektiv hårdvaruimplementering. Detta gör VDF:er väsentliga för modern adaptiv kommunikationsteknik. Den här avhandlingen fokuserar främst på design och implementeringstekniker med låg komplexitet för VDF:er och presenterar tre huvudsakliga bidrag. För det första föreslår den tre VDF-realiseringar för samtidig lågpassfiltrering och utjämning med användning av polynomkanalmodeller, med systematiska designprocedurer baserade på minimax optimering för alla föreslagna strukturer. Dessutom presenteras en snabb designmetod för VDF:erna med flera variabla parametrar, som avsevärt kan minska designtiden. För det andra introducerar den frekvensdomänimplementationer av VDF:er med överlappningssparateknik. Baserat på antagandet att dessa filter har utformats med användning av en gemensam designmetod baserad på optimering av impulssvarskoefficienterna, föreslås filtrets DFT-koefficienter implementeras som fasta, hybrida eller variabla vikter. Slutligen presenterar avhandlingen en effektiv designansats för ett digitalt filter med variabel bandbredd implementerat i frekvensdomänen med användning av överlappningssparametoden. Det föreslagna tillvägagångssättet är baserat på en hybrid av frekvenssampling och optimering, vilket möjliggör direkt optimering av DFT-koefficienterna med tanke på implementeringen av filterfrekvensdomänen och därigenom märkbart minska kostnaden för implementering och en onlineuppdatering av DFT-filterkoefficienterna när bandbredden är varierande.
Optimum envelope-constrained filter design is concerned with time-domain synthesis of a filter such that its response to a specific input signal stays within prescribed upper and lower bounds, while minimizing the impact of input noise on the filter output or the impact of the shaped signal on other systems depending on the application. In many practical applications, such as in TV channel equalization, digital transmission, and pulse compression applied to radar, sonar and detection, the soft least square approach, which attempts to match the output waveform with a specific desired pulse, is not the most suitable one. Instead, it becomes necessary to ensure that the response stays within the hard envelope constraints defined by a set of continuous inequality constraints. The main advantage of using the hard envelope-constrained filter formulation is that it admits a whole set of allowable outputs. From this set one can then choose the one which results in the minimization of a cost function appropriate to the application at hand. The signal shaping problems so formulated are semi-infinite optimization problems. This monograph presents in a unified manner results that have been generated over the past several years and are scattered in the research literature. The material covered in the monograph includes problem formulation, numerical optimization algorithms, filter robustness issues and practical examples of the application of envelope constrained filter design. Audience: Postgraduate students, researchers in optimization and telecommunications engineering, and applied mathematicians.