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Über dieses Buch

Feedback-Based Orthogonal Digital Filters: Theory, Applications, and Implementation develops the theory of a feedback-based orthogonal digital filter and examines several applications where the filter topology leads to a simple and efficient solution. The development of the filter structure is linked to concepts in observer theory. Several signal processing problems can be represented as estimation problems, where a parametric representation of the input is used, to try and replicate it locally. This estimation problem can be solved using an identity observer, and the filter topology falls in this framework. Hence the filter topology represents a universal building block that can find application in several problems, such as spectral estimation, time-recursive computation of transforms, etc. Further, because of the orthogonality constraints satisfied by the structure, it also represents a robust solution under finite precision conditions.
The book also presents the observer-based viewpoint of several signal processing problems, and shows that problems that are typically treated independently in the literature are in fact linked and can be cast in a single unified framework. In addition to examining the theoretical issues, the book describes practical issues related to a hardware implementation of the building block, in both the digital and analog domain. On the digital side, issues relating to implementation using semi-custom chips (FPGA's), and ASIC design are examined. On the analog side, the design and testing of a fabricated chip, that functions as a multi-sinusoidal phase-locked-loop, are described.
Feedback-Based Orthogonal Digital Filters serves as an excellent reference. May be used as a text for advanced courses on the subject.

Inhaltsverzeichnis

Frontmatter

1. Introduction

Abstract
Signal processing is a ubiqutous aspect of most systems today, typically with the systems being so complex that not just one, but several signal processing tasks are required to be performed by the system. For instance, some possible tasks are, filtering, equalization, parameter estimation, data compression (transforms, subband coding), etc. These problems have typically been dealt with seperately in the past, and though several solutions have been proposed to each of these problems, no attempt has been made to develop a unified solution. The merit of a unified solution is that it would represent a ‘universal-building-block’ (UBB), that could be used to solve a host of problems.
Mukund Padmanabhan, Ken Martin, Gábor Péceli

2. The Feedback-Based Orthogonal Filter Structure

Abstract
In this chapter, we will apply the observer-based perspective to the problem of digital filtering and design a filter structure that has good properties under finite precision conditions. As of date, there are several digital filter structures that provide good behavior under these conditions [Pec89, PM93, MR76, Fet86, GM75, DD80, DvdV19, RK84, VM84, JLK79, BF77]. A common feature of several of these filter structures is that they fall under the category of “orthogonal” digital filters [Fet88]. Here, the word “orthogonal” is used in the following context: the transfer functions from the input to the states of the filter are orthonormal, or in other words, the Controllability Grammian of the filter is the identity matrix (these structures are also called input-normal form); additionally, if the filter structure realizes an allpass transfer function, the transfer functions from the filter states to its output are also orthonormal (the Observability Grammian is also the identity matrix) (structures with an identity Observability Grammian are also called output-normal form). In earlier literature, the term “orthogonal” has also been used in a different context: to characterize filters that are realized as terminated two-ports, with the two-port having a unitary transfer matrix [DD80, DvdV19, RK84]. In the following text, ‘orthogonal2’ will be used when referring to this type of orthogonality1.
Mukund Padmanabhan, Ken Martin, Gábor Péceli

3. Computation of Time-Recursive Transforms

Abstract
In this chapter, we primarily examine the problem of computing an N * N transform on an input vector, in a time-recursive manner, and show how the feedback-based structure may be used for this application. The N * N transforms, in general, provide alternative signal representations which may be helpful in solving signal characterization problems, or in the efficient calculation of convolutions. The special signal characterizations are often combined with appropriate data compression techniques, and the concept of evaluating convolutions in the transformed domain, is extended to other signal processing techniques, as well.
Mukund Padmanabhan, Ken Martin, Gábor Péceli

4. Spectral Estimation

Abstract
In this chapter, we consider the problem of spectral estimation and line enhancement. To simplify matters, we will assume throughout the chapter that the input is a multi-sinusoidal signal; such a signal could be produced by a hypothetical system comprising of a parallel bank of resonators, and our objective is not only to estimate the frequencies of these resonators but also to isolate the outputs of the different resonators i.e., the different components of the multi-sinusoidal signal. In short, we would like to locally reconstruct the various components of the input signal. Let us assume for a moment that we know the frequencies of the various components i.e., the configuration of the hypothetical system is known. The problem of local regeneration of the components now simply becomes one of setting the initial states of the resonators of the hypothetical system to the right value.
Mukund Padmanabhan, Ken Martin, Gábor Péceli

5. Hardware Implementation

Abstract
In the previous chapters, we discussed the theory and application of various signal processing blocks that fall in the framework of an observer. In this chapter, we will consider hardware implementations of some of these signal-processing blocks.
Mukund Padmanabhan, Ken Martin, Gábor Péceli

Backmatter

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