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This book is a very concise introduction to recursive digital filters. The goal is to get the reader to the point where he or she can understand and use these filters as quickly as possible. To accomplish this we have kept the amount of mathematical background material to a minimum and have included many examples. But make no mistake, this is not a book for dummies or complete idiots. Some degree of mathematical sophistication is required. If you have never used complex numbers and do not know what Euler's identity is, then this book is not for you. If you have a basic physical science mathematics background, then you should have no problem with this book. We start with a short introduction to the minimum mathematics required to describe, use, and design recursive digital filters. This includes a description of the z-transform, filter system functions, and the frequency response. This is followed by examples of the simplest possible low pass, high pass, band pass, and band stop filters. There are examples showing how to use all these filters. A section on band stop filter banks is also included. The design portion of the book covers impulse invariance and bilinear transform design. We give a minimum theoretical description of these methods and plenty of examples. For the bilinear transform method we show how to turn analog low pass Butterworth filters into digital low pass, high pass, band pass, and band stop filters. Being able to convert analog filters to digital is useful because analog filter design is a more mature and well understood subject. The final section of the book is on analog Butterworth filters. The filter software used in this book is written by the authors, and is available free on the book's web page at http: //www.abrazol.com/books/filter1/ The programs are written in the C programming language, and will have to be compiled before you can use them. You do not have to know C to use the programs or understand the contents of the book. There is a C language compiler for every major operating system. A good one that is also free is gcc. Some of these programs have also been converted to the awk scripting language.

There are 50 unique patterns in this book, each on its own physical page. The authors have for many years been obsessed with finding patterns in nature and in mathematics. This is just a very small sample of some of the interesting patterns they have discovered. The patterns are named after the German mathematician Elwin Bruno Christoffel (1829-1900). He did not directly produce them, but they are related to some of his work. Details on how the patterns are created can be found in the book Pattern Generation for Computational Art.

This book is the result of a lifelong love of music and an obsession with patterns. The authors have for many years been exploring methods to find, create, describe and analyze patterns. They wrote this book to show how some of these methods can be used to generate rhythms. The methods can produce an almost endless variety of new rhythms along with popular traditional ones. For a lover of music what could be more wonderful than that? The study of patterns at anything beyond a superficial level does require some mathematics. Fortunately the mathematics can be kept at a very elementary level. Anyone comfortable with a little algebra should have no trouble understanding and using these rhythm generation methods. Only the last chapter on stochastic rhythms requires a bit more than elementary mathematics. Any reader who faints at the sight of an equation should probably not buy the book. The book has many example rhythms for which there are MIDI files that you can listen to on the book's website: abrazol.com/books/rhythm1/. There you can also find free software for generating rhythms, doing calculations, and creating MIDI files.

This book shows how to turn computer generated number sequences into intricate visual patterns. The sequences are strings of the binary numbers 0 and 1 which are translated into drawing instructions to produce beautiful patterns. These patterns provide a glimpse of the hidden platonic world of mathematics. The book starts with Christoffel words and Sturmian sequences which are derived from the continued fraction expansion of rational and irrational numbers. How this is done is explained very clearly in the book and very little mathematical background is required from the reader. The book moves on to Automatic sequences such as the Thue-Morse and Rudin-Shapiro sequences which are various ways of calculating digital roots of the integers. The first part of the book ends with sequences generated by folding paper. Translating a sequence into drawing instructions is done using a finite automaton. This is a very general method for translating sequences that allows the same sequence to produce many different patterns. No prior experience with finite automata is necessary. All the background needed is explained in the book. The second part of the book is devoted to L-systems which is another way of producing a string of drawing instructions. Here the strings are produced by an iterative symbol substitution process. The images produced often have a self similar fractal structure. It is possible to create many images that resemble plants. The book shows how to use an automaton and context free grammars to systematically look at all L-systems of a particular type. All software used to create the sequences and images in the book are free for readers to download from the book's website at: http: //www.abrazol.com/books/patterngen/ The software consists of small programs written in the C programming language that can be run on all major operating systems. Inside the book are 327 images serving as inspiration for the kinds of images you can create. There are an infinite variety of images you can generate using the software that comes with this book, providing a computational image generation lab.

This is a book about solving problems related to automata and regular expressions. It helps you learn the subject in the most effective way possible, through problem solving. There are 84 problems with solutions. The introduction provides some background information on automata, regular expressions, and generating functions. The inclusion of generating functions is one of the unique features of this book. Few computer science books cover the topic of generating functions for automata and there are only a handful of combinatorics books that mention it. This is unfortunate since we believe the connection between computer science and combinatorics, that is opened up by these generating functions, can enrich both subjects and lead to new methods and applications. We cover a few interesting classes of problems for finite state automata and then show some examples of infinite state automata and recursive regular expressions. The final problem in the book involves constructing a recursive regular expression for matching regular expressions. This book explains: * Why automata are important. * The relationship of automata to regular expressions. * The difference between deterministic and nondeterministic automata. * How to get the regular expression from an automaton. * Why two seemingly different regular expressions can belong to the same automaton. * How the regular expression for an infinite automaton is different than one for a finite one. * The relationship of a regular expression to a regular language. * What a generating function for a language tells you about the language. * How to get a generating function from a regular expression. * How the generating function of a recursive regular expression is different from that of an ordinary regular expression. * How to test divisibility properties of integers (binary and decimal based) using automata. * How to construct an automaton to search for a given pattern, or for a given pattern not occurring. * How to construct an automaton for arbitrary patterns and alphabets. * How the recursive regular expression for nested parentheses leads to the Catalan numbers. Included in this book: * Divisibility problems in binary and decimal. * Pattern search problems in binary, ternary, and quaternary alphabets. * Pattern search problems for circular strings that contain or do not contain a given pattern. * Automata, regular expressions, and generating functions for gambling games. * Automata and generating functions for finite and infinite correctly nested parentheses. * The recursive regular expression for matching regular expressions over a binary alphabet. * A further reading list.

The discovery of nuclear magnetic resonance earned Felix Bloch and Ed Purcell the 1952 Nobel Prize in Physics. What their discovery took advantage of, is that protons are the world's smallest magnets. These tiny magnets can also be used to make a magnetometer, of the type described in this book.This book describes how to build a proton precession magnetometer, suitable for measurements of the Earth's magnetic field. This method of measuring magnetic fields offers the theoretically highest possible precision, limited only by the known value of the gyromagnetic ratio of the proton.Uses of the magnetometer include: making precise measurements of the Earth's magnetic field, calibrating low field magnetometers, teaching modern signal processing techniques, demonstrating nuclear magnetism and NMR to students, and measuring nuclear magnetic relaxation in liquids.The Earth's field proton precession magnetometer, called the Magnum, described in this book, was formerly a commercial product, developed and sold by Exstrom Laboratories LLC. It was designed by Stefan Hollos and Richard Hollos.

This book should allow anyone with basic electronics skills to quickly design a passive Butterworth filter. All possible low pass and high pass filters up to tenth order, and all possible band pass and band stop filters up to eighth order are covered. Schematics and component values for these filters are given along with formulas for scaling the values to the particular frequency the filter must operate at. There is a design example for each of the filter types that shows how to scale the component values. A Spice simulation file for the design is given along with the frequency response. If you want band pass or band stop filters higher than eighth order the book explains how to use a low pass filter to construct them. So the information is there to construct filters up to twentieth order but we don't recommend trying to do that. The non ideal nature of the components makes it hard to get the expected extra performance. The website for this book is http: //www.abrazol.com/books/filter2/ where we will post related resources.

Creating Melodies is a companion to our book Creating Rhythms. The book will show you how to explore the infinite space of melodies.Like the rhythms book, it comes with software that you can download from the book's website. With the software you can generate countless new melodies and variations on old ones. Combine those melodies with rhythms from our rhythms book and you have an endless source of inspiration for new music.You can listen to the many example melodies in this book as MIDI and MP3 files on the book's website at http://www.abrazol.com/books/melody1/We had a lot of fun writing this book. In fact it took us so long to write it because it was hard to tear ourselves away from creating so much interesting new music and write up the results. Now you can have fun with it too!