Finite worldlength effects in fixed-point implementations of linear systems

Thesis (M.Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1998.Includes bibliographical references (p. 173-194).by Vinay Mohta.M.Eng

Passive cascaded-lattice structures for low-sensitivity FIR filter design, with applications to filter banks

A class of nonrecursive cascaded-lattice structures is derived, for the implementation of finite-impulse response (FIR) digital filters. The building blocks are lossless and the transfer function can be implemented as a sequence of planar rotations. The structures can be used for the synthesis of any scalar FIR transfer function H(z) with no restriction on the location of zeros; at the same time, all the lattice coefficients have magnitude bounded above by unity. The structures have excellent passband sensitivity because of inherent passivity, and are automatically internally scaled, in an L_2 sense. The ideas are also extended for the realization of a bank of MFIR transfer functions as a cascaded lattice. Applications of these structures in subband coding and in multirate signal processing are outlined. Numerical design examples are included

INVESTIGATION OF ROUNDOFF NOISE IN IIR DIGITAL FILTERS USING MATLAB

As technology increases, more and more devices are becoming digital. The typical purpose of a digital filter is to detect unwanted signals and noise and remove them by filtering. The infinite impulse response (IIR) filter is also called a recursive filter because of the feedback necessary during implementation. A filter can be expressed as a cascade of second-order sections (SOS). For N sections, there are (N!) ways to pair the poles and zeros. There are also (N!) ways to order the resulting second-order sections, for a total of (N!)2 different filter configurations for implementation. In this thesis, for a 6th order filter with three second-order sections, there are (3!)2 or 36 different ordering and pairings. Jackson\u27s proposed a few rules for the pairing of the poles and zeros and the ordering of the second-order sections. These rules were investigated using MATLAB for Butterworth, Chebyshev, and elliptic filter type. Three cutoff frequencies were used to represent the low, mid, and high cutoff frequencies. The value of the low cutoff frequency is .2π. The value of the mid cutoff frequency is .5π. The value of the high cutoff frequency is .8π. The filters were also implemented for both DF1 and DF2. A broad new \u27rule\u27 was not created but a few detailed \u27rules\u27 were suggested depending on the filter type and direct-form implementation

Relationships between digital signal processing and control and estimation theory

Bibliography: leaves 83-97.NASA Grant NGL-22-009-124 and NSF Grant GK-41647.Alan S. Willsky

Digit-slicing architectures for real-time digital filters

One of the many important algorithmic techniques in digital signal processing is real-time digital filtering. Modular sliced structures for digital filters have been proposed before, but the nature of implementation has been mainly constrained to non-recursive second order digital filters with positive values of coefficients. The aim of this research project is to extend this modular digit slicing concept to more practical higher order digital filters which are recursive and are of many forms (direct, nondirect, canonic, non-canonic). [Continues.

NATURAL ALGORITHMS IN DIGITAL FILTER DESIGN

Digital filters are an important part of Digital Signal Processing (DSP), which plays vital roles within the modern world, but their design is a complex task requiring a great deal of specialised knowledge. An analysis of this design process is presented, which identifies opportunities for the application of optimisation. The Genetic Algorithm (GA) and Simulated Annealing are problem-independent and increasingly popular optimisation techniques. They do not require detailed prior knowledge of the nature of a problem, and are unaffected by a discontinuous search space, unlike traditional methods such as calculus and hill-climbing. Potential applications of these techniques to the filter design process are discussed, and presented with practical results. Investigations into the design of Frequency Sampling (FS) Finite Impulse Response (FIR) filters using a hybrid GA/hill-climber proved especially successful, improving on published results. An analysis of the search space for FS filters provided useful information on the performance of the optimisation technique. The ability of the GA to trade off a filter's performance with respect to several design criteria simultaneously, without intervention by the designer, is also investigated. Methods of simplifying the design process by using this technique are presented, together with an analysis of the difficulty of the non-linear FIR filter design problem from a GA perspective. This gave an insight into the fundamental nature of the optimisation problem, and also suggested future improvements. The results gained from these investigations allowed the framework for a potential 'intelligent' filter design system to be proposed, in which embedded expert knowledge, Artificial Intelligence techniques and traditional design methods work together. This could deliver a single tool capable of designing a wide range of filters with minimal human intervention, and of proposing solutions to incomplete problems. It could also provide the basis for the development of tools for other areas of DSP system design

Digital Filtering Algorithms for Decorrelation within Large Least Squares Problems

The GOCE (Gravity Field and steady-state Ocean Circulation Explorer) mission is dedicated to the determination of the Earth's gravity field. During the mission period of at least one year the GOCE satellite will collect approximately 100 million highly correlated observations. The gravity field will be described in terms of approximately 70,000 spherical harmonic coefficients. This leads to a least squares adjustment, in which the design matrix occupies 51 terabytes while the covariance matrix of the observations requires 72,760 terabytes of memory. The very large design matrix is typically computed in parallel using supercomputers like the JUMP (Juelich Multi Processor) supercomputer in Jülich, Germany. However, such a brute force approach does not work for the covariance matrix. Here, we have to exploit certain features of the observations, e.g. that the observations can be interpreted as a stationary time series. This allows for a very sparse representation of the covariance matrix by digital filters. This thesis is concerned with the use of digital filters for decorrelation within large least squares problems. First, it is analyzed, which conditions the observations must meet, such that digital filters can be used to represent their covariance matrix. After that, different filter implementations are introduced and compared with each other, especially with respect to the calculation time of filtering. This is of special concern, as for many applications the very large design matrix has to be filtered at least once. One special problem arising by the use of digital filters is the so-called warm-up effect. For the first time, methods are developed in this thesis for determining the length of the effect and for avoiding this effect. Next, a new algorithm is developed to deal with the problem of short data gaps within the observation time series. Finally, it is investigated which filter methods are best adopted for the application scenario GOCE, and several numerical simulations are performed.Digitale Filteralgorithmen zur Dekorrelation in großen kleinste-Quadrate Problemen Die GOCE (Gravity Field and steady-state Ocean Circulation Explorer) Mission ist der Bestimmung des Erdschwerefeldes gewidmet. Während der Missionsdauer von mindestens einem Jahr wird der GOCE Satellit circa 100 Millionen hoch korrelierte Beobachtungen sammeln. Das Erdschwerefeld wird durch circa 70.000 sphärisch harmonische Koeffizienten beschrieben. Dies führt zu einem kleinste-Quadrate Ausgleich, wobei die Designmatrix 51 Terabytes benötigt während die Kovarianzmatrix der Beobachtungen 72.760 Terabytes erfordert. Die sehr große Designmatrix wird typischerweise parallel berechnet, wobei Supercomputer wie JUMP (Juelich Multi Processor) in Jülich (Deutschland) zum Einsatz kommen. Ein solcher Ansatz, bei dem das Problem durch geballte Rechenleistung gelöst wird, funktioniert bei der Kovarianzmatrix der Beobachtungen nicht mehr. Hier müssen bestimmte Eigenschaften der Beobachtungen ausgenutzt werden, z.B. dass die Beobachtungen als stationäre Zeitreihe aufgefasst werden können. Dies ermöglicht es die Kovarianzmatrix durch digitale Filter zu repräsentieren. Diese Arbeit beschäftigt sich mit der Nutzung von digitalen Filtern zur Dekorrelation in großen kleinste-Quadrate Problemen. Zuerst wird analysiert, welche Bedingungen die Beobachtungen erfüllen müssen, damit digitale Filter zur Repräsentation ihrer Kovarianzmatrix benutzt werden können. Danach werden verschiedene Filterimplementierungen vorgestellt und miteinander verglichen, wobei spezielles Augenmerk auf die Rechenzeit für das Filtern gelegt wird. Dies ist von besonderer Bedeutung, da in vielen Anwendungen die sehr große Designmatrix mindestens einmal gefiltert werden muss. Ein spezielles Problem, welches beim Benutzen der Filter entsteht, ist der sogenannte Warmlaufzeiteffekt. Zum ersten Mal werden in dieser Arbeit Methoden entwickelt, um die Länge des Effekts zu bestimmen und um den Effekt zu vermeiden. Als Nächstes wird ein neuer Algorithmus zur Lösung des Problems von kurzen Datenlücken in der Beobachtungszeitreihe entwickelt. Schließlich wird untersucht, welche Filtermethoden man am besten für das Anwendungsszenario GOCE verwendet und es werden verschiedene numerische Simulationen durchgeführt

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