CHAPTER 2         The Digital Atomic Age


How do you describe the revolution in digital electronics, in the digital life of America, without comparing it to an explosion like the Atomic Bomb?  Even as the inspiring and informative little book ATOMIC AGE PHYSICS describes all the changes in the world and in classical physics as the first man the globe even smaller and the second radically changed into the modern physics of a modified Bohr theory of the atom, quantum mechanics, X-rays, natural radioactivity, and it takes the whole aforementioned book to describe what happened to America and the world.  Even as Henry Steele Commager in THE AMERICAN MIND calls the twentieth century “the watershed of American Thought” centered around a preeminence of science, so the last 50 years in electronics have been such an explosion toward the digital, as for example in digital computers and digital phones, that we look for more than a watershed in American thought and technology comparable to a concept of the Digital Atomic Age.

Technical Applications of Computers

Those of us who were fortunate enough to work 50 years ago with Air Early Warning radars that required the large super-constellations of Lockheed to contain and then computers like the CDC 3600 that required a whole large room to contain, are still fascinated that as we pick up our little laptop digital computers, as big in computing capability as that large CDC3600 with millions of Giga-bytes of hard drive memory in two hard drives, and lots of ROM memory, then connect it to a little microprocessor centered digital telephone with broadband service that we can use any place in the world; and with nothing else connected, as we get on-line thinking we have control of the world, for two hours or so we can operate completely independent of any other connections to the outside world.  In short, the digital explosion is now right there in our hands, and we still have trouble comprehending the significance, or maybe in appreciating it!

Most, except those of us fortunate enough to work with the technical applications of “Pulse Electronics” in radar, or even in atomic and nuclear electronics and instruments as part of physics, did not have the advantage of a gradual transition from analog to digital by way of “Pulse Electronics”; but those electronic circuits called “multivibrators”–astable, monostable, and free-running-as electronics transitioned from vacuum tubes to transistors to ICs {Integrated Circuits}, and Microprocessors {and called such in the analog electronics of such textbooks as ELECTRONICS FOR SCIENTISTS AND ENGINEERS} to flip-flops about the same time as ICs were introduced in the wonderful textbook of LOGIC DESIGN WITH ICS.  Likewise, television has incorporated the technologies of devices and circuits, always making the comparable transitions through the years, of “Pulse Electronics”.

Now every home in America has been invaded by Digital Electronics as the means of transmission by TV stations and reception by home receivers has turned, by law, to digital.  If this explosion or revolution from analogy to digital did not hit your life and home in the telephone, or the digital computer, it did in the digital television.  And what might have been only a revolution in the average home and life, has been nothing short of an atomic bomb, whether they know it or not, in the life of those who makes careers in the technical of technology, such as Technicians, Engineers, Scientists, and Computer Scientists. For example what use to be Engineering Departments in Universities and Colleges is now by and large Engineering and Computer Science; and completely new departments and disciplines where digital software and digital hardware {computers, circuits, and devices} have been started to let the younger generations “come-up” in four or five years with this digital revolution of the last 50 years.

Perhaps you have never thought of your computer software such as windows and Microsoft Office as digital software.  Granted you see it less in those most common  software to the average digital computer user; and before we get into the very technical aspects of such software programmed in the language of C++, with discussions of the levels of software from higher level like C, C++, FORTRAN, BASIC, and MATLAB, to the medium languages of Motorola and IBM assembly language programming, down to the basic level of the language in which the machine called the computer works on, the computer language of the digits of 1 and 0, alias the digital language of the digital machine called the digital computer, we can momentarily be satisfied with these higher languages such as C and MATLAB as requiring a digital computer on which to work.

1-1:  Math led the technical world into the Digital with Linear Algebra.

Of course, in many cases it was not just the pure mathematicians that led the way into the digital revolution with linear algebra, vector analysis, numerical analysis, and the LaPlace transform which changed the analog of differential equations into the digital of a mathematical series, for if you lived through the classes of differential equations, linear algebra, partial differentials equations, and difference equations, or even the matrix and determinants of a good technical math course, you know the two favorite words of pure mathematicians to be “trivial” and “trite”; and it required the applications of many Engineers and Physicists, also technicians and technologies, to force these same mathematics to make such practical applications as we see in this book and in any good book of applications such as ADVANCED APPLICATIONS OF ENGINEERING MATHEMATICS or TECHNICAL APPLICATIONS OF MATH.  Always those leaders in Numerical Analysis, during both the periods of analog applications and of digital applications, were adjusting their technics and applications, likewise their textbooks, as they developed a consistent field of applications with methods such as the Newton-Rapson methods for matrix manipulation and the numerous techniques to convert the analog equations of differential equations into digital math for the digital computer.

  1. Modern Algebra and State Space.
  2. And Operations Research.
  3. Linear Algebra and Vector Analysis.
  4. Simplex Methods of Linear Algebra to Minimization.

1-2:  The Place of Equations in the Digital Revolution.

You have to go all the way back to the physicists like Sir Isaac Newton and George Ohm to appreciate the science and technology of expressing physical and electronics phenomena into the precision of a mathematical equation.  And I am not even sure that they were even called physicists in those days, but in reality were more very practical technologists who desired to describe and control motion or to make batteries for different applications and then describe what happened; and that even as more recently the field of DIGITAL SIGNALS FOR DIGITAL COMMUNICATIONS has been generated in textbooks and universities departments to bring the newer generations up rapidly on the digital revolution in devices, systems, and circuits, so at some point physicists decided to make this first experimenters and discoverers part of their scientific discipline.  {The so-called scientific method is great as an idea and goal, but what you will find in any study of the history of science and scientific thought, is that many discoveries were found by accident.  It is only that the discoveries like Currie in natural radioactivity had the attitude and training to know what to do with those accidents of the lab.}

1-3:  Most Physical Phenomenon is Analog, Requiring Conversion to Digital.

Most physical phenomenon that man tries to monitor and control is analog such as sound, physical motion, electron motion, nuclear radiation, X-rays and other transmissions of the electromagnetic spectrum such as light, infrared, and heat; also water flow and the motion of modern vehicles such as cars, trucks, airplanes, missiles, and spacecraft; so that as technical man saw the need for the digital of digital circuits, devices, and systems such as the computer, it naturally occurred to him like the caveman in the wilderness about the necessity of a wheel, that there would have to circuits and systems for conversion for the natural analog phenomenon to the digital circuits and systems if man was to be able to monitor and control the physical phenomenon of the universe.  Even as INSTRUMENTS AND CONTROLS have been an early discipline in technology and engineering, so technical man has been pushed by devices and instruments to control and monitor in every discipline of science and technology; and in turn that revolution of the digital has been an increased part of instruments and control.

1-5:  The Math of Motion is a Good Starting Place for the Technical.

Indeed, physical motion as described in the mathematical equations of differential equations is not only a good starting place for the technical applications of digital computers, but has analogous equations in most other disciplines of physics such as electricity, heat and thermodynamics, nuclear, and light.  {The first and fundamental discipline of physics called “mechanics” is about the equations and physical phenomenon of motion such as velocity, acceleration, mass, and force.}

1-6:  Digital and Digital Computers to Technical Applications of Computers.

This book on TECHNICAL APPLICATIONS OF COMPUTERS WITH MATLAB AND SIMULINK narrows the fields of the digital, digital math, and digital computers to those applications of the contemporary digital computer to the description and solution of technical problems.  In other words, the common usages of the computer in the homes and office where the internet and Microsoft office, in the schools, and in business applications is not covered except vaguely.

There will be a few other examples of technical applications from the computer languages of BASIC, FORTRAN, and some assembly languages; but by and large, this textbook is focused on the higher language of MATLAB.  MATLAB especially with the simulation software that comes with it of SIMULINK, can do everything except sing for you; and in this text, we will strive to also make it sing for you, especially if you have an e-book version of the text in PDF {the Portable Document Format of Adobe}, which can read and sing for you.

1-7:  “Digital Signal Processing”.

Just like educators and engineers developed the disciplines of “Digital Computers” as computers evolved from the analog type to the digital type, and digital electronics as ICs and flip flops replaced transistors and multivibrators, and even physics incorporated all the history of discoveries before them, so the writers of textbooks today have generated a field called “Digital Signal Processing” to keep up with the digital revolution, and to make it understandable by the younger generations not fortunate enough to live through it.  I want you to know by way of a proper perspective of the history of technology, that these aspects of the digital revolution developed quite naturally and independent of any such discipline of study; however, that the organized manner in which the authors now describe the random nature of the past history of the digital, while giving you the false concept that an Einstein of digital electronics sat down to figure it out ahead of time and history, it does help to get it all together in one textbook such as DIGITAL SIGNAL PROCESSING, A Computer-Based Approach” by Sanjit K. Mitra, of the Department of Electrical and Computer Engineering at the University of California, Santa Barbara and McGraw_Hill Irwin in the “McGrawHill Series in Electrical and Computer Engineering”

By the way, where engineering and technology are today, and how it fits in with digital, digital electronics, and computers can be seen by the other books in the McGraw-Hill series; and you of electronics technology and electronics engineering technology will recall many similar McGraw-Hill books:  (1) Circuits and Systems {one good book on “Integrated Electronics” combined the circuits with the systems and then went on into ICs where the circuit and circuits, even systems do become the device}; (2) Communications and Signal Processing {before Digital Processing there was just “Signal Processing” with both analog and digital, more so analog like in radio and television, or even the Telemetry of more technical applications just as in the flight test of missiles and airplanes, also the test of weather with  balloons}, and even now among the many toolboxes that are available with MATLAB such as “Control” are those of “Signal Processing” and “Digital Signal Processing”; (3) Computer Engineering {most students will remember a first book on Digital Computers by Bartee called FUNDAMENTALS OF DIGITAL COMPUTERS}; (4) Control Theory and Robotics; (5) Electromagnetics; (6) Electronics and VLSI  Circuits {Very Large Systems Integration as ICs have gone from small scale, to medium scale to large and very large systems of circuits integration}; (5) Introductory; (6) Power; and (6) Antennas, Microwaves, and Radar.

McGraw-Hill and other good publishers {although too expensive today for the average student} provided many textbooks for electronics technology correlated with such curriculum courses as:  (1).  Basics of Electronics and Electronic Amplifiers; (2) Fundamentals of Electricity and Electrical Circuits; (3) Instruments and Measurements {like in the text by Soisson}; (4) Analog and Digital Computers; (5) Microwaves and Measurements; and (6) Communications {centering around radio and TV}.

  1. Digital over Analog. Why, students of technical applications through the more recent years in technology, have asked, “Do we need digital and digital circuits and systems, since most natural phenomenon that we desire to monitor and control are analog signals, and more hardware is required to convert from analog to digital and then back from digital to analog when a human wants to interpret and understand the original signals?  Good question!  One of the most significant areas of organization of past history the textbook writers in “Digital Signal Processing” have provided for us is in their through discussions and treatment of the necessity and importance of the digital over the analog in electronics.
  2. Analog Math to Digital Math. The disciple of Digital Signal Processing provides the digital math required to explain and control digital electronics.
  3. Techniques of Numerical Analysis. The discipline of Digital Signal Processing supplements the field of Numerical Analysis to provide us with digital mathematical techniques for applications of digital computers.
  4. It keeps us honest. That is, those of us who lived through the digital revolution in a very practical and applied manner are kept honest by the research and study of the discipline of ““Digital Signal Processing”, also the history; and in fact, we will return the favor!  Throughout this very practical textbook on the technical applications of digital computers possible with MATLAB and SIMULINK, and a concentration of those applications right now as pushed by the currently applied state of the art, the right now applications will be given priority over any history and textbook on such disciplines.  And, in fact, much of this discipline of “Digital Signal Processing”, primarily for graduate engineers, although geared down to the more practical level of electronics engineering technology and technical applications like in computer science, will be correlated with TECHNICAL APPLICATIONS OF COMPUTERS WITH MATLAB AND SIMULINK, where applicable.

1-8:  (D1)  MATLAB, Path, and Workspace.

{RAY sect 1}

Here at the beginning of this book on TECHNICAL APPLICATIONS OF COMPUTERS with MATLAB and Simulink is an excellent place to drill on the pros and cons of MATLAB value.  First and foremost, it is a language designed for technical computing as say contrasted to business; more specifically for the calculations of mathematics {a chapter is on Differential Equations and another on State Space}1, for data analysis {and report writing which is THE application process of one chapter}, and to visual math operations say for example in plotting and data analysis in a multitude of plots.

Programming is easy and rapid in MATLAB.  Besides the simple access of a edit window to create or change a large or small script with the typing of “edit” in the command window, there is the ability to download or otherwise save and call up any .m file, .dat file, and so on.  Many technical books with MATLAB come equipped with a CD with many .m files to illustrate the programming of the book, or reference a place online or address where you can secure the accompanying .m files.

Even though MATLAB has similar programming features as the C language, it is slower; however, the consolation is that MATLAB scripts can quickly be converted into C language with the appropriate C compiler, and provisions are provided in the MATLAB environment for creation

  1. Actually besides an initial boost from Linear Algebra, the use of State Space Equations got their foothold largely with computers about the 1980s, in particular the Operational Research techniques for computers and use of CMEX files.

And Simulink–built into the MATLAB environment, and rapidly available with the typing of “Simulink” in the command window–can be used for modeling and/ or simulation.  One of the application chapters is entitled “Model Based Design” which uses blocks in a Simulink window to design a system from which the algorithm can be automatically be delivered for the system program.  For example, avionics companies like Honeywell, Sypris, and Rockwell are now designing a system with blocks in Simulink, or another block based design tool, then outputting from the command window the steps of the software program to run a MFD in the aircraft for monitoring and control.  {Quite often now a software program is loaded into a Computer or Multifunction Display (MFD), to replace the control of the unit by hardware or firmware, and this is called and embedded system or hardware.}  Increasing if you are in missiles or aircraft, you are hearing about GAINS for navigation and control, which stands for GPS Aided Inertia Navigation.  The GPS system is quite often embedded as software in the Inertial Guidance System so that the accuracy can be obtained of a mixture and selection from both GPS satellite signals and the onboard Inertial Navigation System based on an accurate gyro.

MATLAB is not always the best choice for speed of a simulation.  It can take 10-15 minutes for the simulation of a medium size system simulation.  Thus you will see good authors like Brian and Stevens using both FORTRAN and MATLAB in their simulations as we will do in the next chapter on F16 simulations.

  1. DRILL with MATLAB startup.
  2. Type “edit matlabrc.m” and you can read the automatic startup file when MATLAB is started.  Do not edit it, however, only note that the automatically does things like:  (1) set up your current MATLAB path , (2) sets the default figure size for making your plots {you can modify this if you wish}, and (3) provides some helpful hints for getting started like to type “helpwin”, “helpdesk”, or demo.  {Many helpful demos are provided by Mathworks; for example the one on the F-14 computer that we will utilize to start the next chapter on F-16 simulations.}
  3. Close the window in edit for “”.
  4. Type respectively the commands “helpwin”, “helpdesk”, and “demo” in the command window. {Just “help” will provide the same info, but helpwin allows you to double click on any topic for instance information, and other options.}
  5. Type “edit startup.m” in the command window.

Even as this book is a book on the “Technical Applications” of Computers, as contrasted to computers for things like games, email, and video-even standard office and business applications–so MATLAB, like FORTRAN is a language for technical computing.  FORTRAN is faster–the reason we used it for simulation of the F-16 and other aircraft–and cheaper now that older versions of FORTRAN like FORTRAN 95 with a windows interface like Plato is cheaper; but MATLAB is much easier to use and has much more versatility.  Of course you will recognize them both as high-level and interpretative language.  The “M-files” of MATLAB are ASCII files containing MATLAB code, and there are two types of M-files:  scripts which are really small or larger programs, and functions.  A couple of the rules for M-file filenames would include:  (1) the name must be 31 characters or less; (2) must start with a letter, not a number or symbol; and (3) the extension must be “.m”.  It is possible to use any ASCII editor to create and/or edit M-files.  {The default MATLAB editor for editing and debugging M-files is medit.exe.  It automatic comes up with a new window with the simple typing of “edit” in the command window.}

There are 2 ways to call up an M-file:  (1)  type the name of the file in the command window, or (2) it is possible to call up a M-file from within another M-file, like you are accustomed to in FORTRAN with the call to a subroutine.  It is necessary that the called M-file is in the current working directory or on the MATLAB path.

  1. Type the “which” command to determine where a certain M=file resides.

In Command Window:                             EDU» which ADC_F16


Comment:  Looking for the M-file of ADC_F16, the answer comes back from “which ADC_F16” comes back as C drive, directory of 16 simulator, and “ADC_F16.m”.

  1. Definition of and explanation of MATLAB “scripts”: they are ASCII files containing only legitimate MATLAB commands; they execute as the proper filename is typed in the command in down; scripts do not have output and input arguments; scripts operate on data either already in the workspace or on data created as the script progresses {as created, for example x = 22, both x and 22 go into the workspace.
  2. Convert the following FORTRAN parameters as data in MATLAB and then check what is in the workspace by typing “who” in the command line.

PARAMETER (AXX=9496.0,AYY=55814.0,AZZ=63100.0,AXZ=982.0)




Axx = 9496.0; Ayy = 55814.00; A

In Command Window:

1-9:  (D2)  Plotting, Subplots, Axis and Labels.

{ BASICS p 12}

1-10: (D3)  Polynomial Algebra and Polynomial Roots.

{INTRO p 64}

1-11: (D4) Graphics and Descriptive Stats.

{DATA p 4}



Categories: TAC

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