The role of lossless systems in modern digital signal processing: a tutorial

A self-contained discussion of discrete-time lossless systems and their properties and relevance in digital signal processing is presented. The basic concept of losslessness is introduced, and several algebraic properties of lossless systems are studied. An understanding of these properties is crucial in order to exploit the rich usefulness of lossless systems in digital signal processing. Since lossless systems typically have many input and output terminals, a brief review of multiinput multioutput systems is included. The most general form of a rational lossless transfer matrix is presented along with synthesis procedures for the FIR (finite impulse response) case. Some applications of lossless systems in signal processing are presented

A new class of two-channel biorthogonal filter banks and wavelet bases

We propose a novel framework for a new class of two-channel biorthogonal filter banks. The framework covers two useful subclasses: i) causal stable IIR filter banks. ii) linear phase FIR filter banks. There exists a very efficient structurally perfect reconstruction implementation for such a class. Filter banks of high frequency selectivity can be achieved by using the proposed framework with low complexity. The properties of such a class are discussed in detail. The design of the analysis/synthesis systems reduces to the design of a single transfer function. Very simple design methods are given both for FIR and IIR cases. Zeros of arbitrary multiplicity at aliasing frequency can be easily imposed, for the purpose of generating wavelets with regularity property. In the IIR case, two new classes of IIR maximally flat filters different from Butterworth filters are introduced. The filter coefficients are given in closed form. The wavelet bases corresponding to the biorthogonal systems are generated. the authors also provide a novel mapping of the proposed 1-D framework into 2-D. The mapping preserves the following: i) perfect reconstruction; ii) stability in the IIR case; iii) linear phase in the FIR case; iv) zeros at aliasing frequency; v) frequency characteristic of the filters

Studies on Implementation of . . . High Throughput and Low Power Consumption

In this thesis we discuss design and implementation of frequency selective digital filters with high throughput and low power consumption. The thesis includes proposed arithmetic transformations of lattice wave digital filters that aim at increasing the throughput and reduce the power consumption of the filter implementation. The thesis also includes two case studies where digital filters with high throughput and low power consumption are required. A method for obtaining high throughput as well as reduced power consumption of digital filters is arithmetic transformation of the filter structure. In this thesis arithmetic transformations of first- and second-order Richards’ allpass sections composed by symmetric two-port adaptors and implemented using carry-save arithmetic are proposed. Such filter sections can be used for implementation of lattice wave digital filters and bireciprocal lattice wave digital filters. The latter structures are efficient for implementation of interpolators and decimators by factors of two. Th

Digital Filters

The new technology advances provide that a great number of system signals can be easily measured with a low cost. The main problem is that usually only a fraction of the signal is useful for different purposes, for example maintenance, DVD-recorders, computers, electric/electronic circuits, econometric, optimization, etc. Digital filters are the most versatile, practical and effective methods for extracting the information necessary from the signal. They can be dynamic, so they can be automatically or manually adjusted to the external and internal conditions. Presented in this book are the most advanced digital filters including different case studies and the most relevant literature

Low passband sensitivity digital filters: A generalized viewpoint and synthesis procedures

The concepts of losslessness and maximum available power are basic to the low-sensitivity properties of doubly terminated lossless networks of the continuous-time domain. Based on similar concepts, we develop a new theory for low-sensitivity discrete-time filter structures. The mathematical setup for the development is the bounded-real property of transfer functions and matrices. Starting from this property, we derive procedures for the synthesis of any stable digital filter transfer function by means of a low-sensitivity structure. Most of the structures generated by this approach are interconnections of a basic building block called digital "two-pair," and each two-pair is characterized by a lossless bounded-real (LBR) transfer matrix. The theory and synthesis procedures also cover special cases such as wave digital filters, which are derived from continuous-time networks, and digital lattice structures, which are closely related to unit elements of distributed network theory

Digital Filters and Signal Processing

Digital filters, together with signal processing, are being employed in the new technologies and information systems, and are implemented in different areas and applications. Digital filters and signal processing are used with no costs and they can be adapted to different cases with great flexibility and reliability. This book presents advanced developments in digital filters and signal process methods covering different cases studies. They present the main essence of the subject, with the principal approaches to the most recent mathematical models that are being employed worldwide

Frequency-warped autoregressive modeling and filtering

This thesis consists of an introduction and nine articles. The articles are related to the application of frequency-warping techniques to audio signal processing, and in particular, predictive coding of wideband audio signals. The introduction reviews the literature and summarizes the results of the articles. Frequency-warping, or simply warping techniques are based on a modification of a conventional signal processing system so that the inherent frequency representation in the system is changed. It is demonstrated that this may be done for basically all traditional signal processing algorithms. In audio applications it is beneficial to modify the system so that the new frequency representation is close to that of human hearing. One of the articles is a tutorial paper on the use of warping techniques in audio applications. Majority of the articles studies warped linear prediction, WLP, and its use in wideband audio coding. It is proposed that warped linear prediction would be particularly attractive method for low-delay wideband audio coding. Warping techniques are also applied to various modifications of classical linear predictive coding techniques. This was made possible partly by the introduction of a class of new implementation techniques for recursive filters in one of the articles. The proposed implementation algorithm for recursive filters having delay-free loops is a generic technique. This inspired to write an article which introduces a generalized warped linear predictive coding scheme. One example of the generalized approach is a linear predictive algorithm using almost logarithmic frequency representation.reviewe

Switched-current filtering systems: design, synthesis and software development

Allpass filters are commonly employed in many applications to perform group delay equalisation in the passband. They are non-minimum phase by definition and are characterised by poles and zeros in mirror-image symmetry. SI allpass filters of both cascade biquad and bilinear-LDI ladder types have been in existence. These were implemented using Euler based integrators. Cascade biquads are known to have highly sensitive amplitude responses and Euler integrators suffer from excess phase. The equalisers that are proposed here are based on bilinear integrators instead of Euler ones. Derivation of these equalisers can proceed from either the s-domain, or directly from the z-domain, where a prototype is synthesised using the respective continued-fractions expansions, and simulated using standard matrix methods. The amplitude response of the bilinear allpass filter is shown to be completely insensitive to deviations in the reactive ladder section. Simulations of sensitivities and non-ideal responses reveal the advantages and disadvantages of the various structures. Existing DI multirate filters have to date been implemented as direct-form FIR and IIR polyphase structures, or as simple cascade biquad or ladder structures with non-optimum settling times. FIR structures require a large number of impulse coefficients to realise highly selective responses. Even in the case of linear phase response with symmetric impulse coefficients, when the number of coefficients can be halved, significant overheads can be incurred by additional multiplexing circuitry. Direct-form IIR structures are simple but are known to be sensitive to coefficient deviations and structures with non-optimum settling times operate entirely at the higher clock frequency. The novel SI decimators and interpolators proposed are based on low sensitivity ladder structures coupled with FIR polyphase networks. They operate entirely at the lower clock frequency which maximises the time available for the memory cells to settle. Two different coupling architectures with different advantages and disadvantages are studied