From Professor Irving Kalet….

This is a post written by Professor Kalet:

Analog Modulation-Back to the Future?

Or was Armstrong’s Frequency Modulation the “Last Word” in Analog Modulation

In recent times there has been a renewed interest in Edwin Armstrong, his work, his career and his life. This “blog” is probably the best evidence of that renewed interest.

A few years ago I also became interested, or rather “re-interested” in Armstrong’s work on frequency modulation (FM).

Many years earlier when I was studying for my doctorate here at Columbia University, I had decided that I was going to discover a better analog modulation than FM. I was going to outdo Armstrong!

Luckily for me, my thesis advisor, the late Professor William R. Bennett, asked me a very simple question, “How do you know that there is a better analog modulation than FM?” And so he sent me back to the drawing board to find the bounds on analog modulation, based on information theory.

This I did, and so did someone else at MIT, named Tom Cruise, yes, Tom Cruise, but not that Tom Cruise!

Both of us came up [1, 2] with basically the same result. Our work was essentially an extension of an earlier paper by Goblick [3]. Our work (also to be found in Van Trees’ book [4]) showed, that at least theoretically there is a possibility of an analog modulation (or at least a transmission technique for analog sources), which may outperform FM. In fact, the actual results predicted by information theory can more or less be achieved by a digital communications scheme, which utilizes a good quantization scheme for the analog source, a good modulation scheme, e.g., QAM for transmitting the bits and a good code like a turbo-code, or an LDPC code, for improving error probability. However, these results are really based on converting the analog information source into bits and then using digital communications to transmit the bits.

What interested me years ago and what has re-kindled my interest now, is the old question as whether some truly analog phase (or frequency) modulation, or combined amplitude-phase analog modulation scheme, can be found which approaches the bounds predicted by information theory.

As far as I can recollect, the only real serious efforts, to find better analog,  (or at least different analog) modulations, since Armstrong’s monumental work in the mid 1930’s, was the work of Boardman and Van Trees, on Optimum Angle Modulation [5], in the late 1960’s, which involved the optimization of linear phase (or frequency) modulation with a bandwidth constraint. There was also some work done on the so-called “single-sideband FM” concept [6], also in the 1960’s. And again, during the 1960’s there was an attempt by Voelcker to look at the modulation process using a unified approach. He called this a “Unified Theory of Modulation” [7,8].   

However, as is well known, since the 1960’s the world has gone digital, even to the point of having only digital television broadcasting in the United States.

The reader might ask the following reasonable question, “Why look at analog modulation again after so many years?”

Well, the simple answer to that question could just be, “Why not?”

The fact that there might be a chance for an improved analog modulation is of itself (in my opinion!) an interesting question for any researcher in communications.

However, there may be other practical reasons as well. As mentioned earlier, it is more than forty years since there has been any serious research into analog modulation. During this period of time, there has been a phenomenal development in the implementation of communication systems. The fields of integrated circuits and circuit miniaturization have allowed the development of digital signal processing beyond belief. There have also been unbelievable advancements in analog processing and circuitry, allowing miniaturization of analog circuits. Furthermore, many of the sources of transmitted information are still analog in nature, e.g., voice and music.

If new analog modulation techniques were to be invented, it may now be possible to cheaply implement these ideas with the new technologies, developed in the past forty years.

Another interesting question might be, “How do we apply new concepts which have arisen in digital communications, such as multi-imput multiple output (MIMO) antenna arrays, to analog communications?”

I guess what I am asking the readers of this blog is whether any of you are still interested in analog modulation, or has analog modulation gone the way of the “horse and buggy”, and the “dial-up” telephone” ?

I would be interested in hearing any comments from anyone out there??

Irving Kalet


  1. T. J. Cruise, Channel capacity for a RMS bandwidth constraint”, MIT, Research Laboratory of Electronics, Quarterly Progress Report, July 1968, pp. 201-205.
  2. I. Kalet, “Bounds on optimum analog modulation over gaussian channel with second-moment bandwidth constraints”, Proceedings IEEE International Conference on Information Theory, Ellenville, N.Y., January 1969.
  3. T. J. Goblick, Jr., “Theoretical limitations on the transmission of data from analog sources”, IEEE Transactions on Information Theory, Vol. 11, No. 4, October 1965, pp. 558-567.
  4. H. L. Van Trees, “Detection, Estimation and Modulation Theory-Nonlinear Modulation Theory, Part II”, J. Wiley and Sons, 1971, Chapter V.
  5. C. J. Boardman and H. L. Van Trees, “Optimum angle modulation”, IEEE Transactions on Comm. Tech., Vol. 13, December 1965, pp. 452-464.
  6. R. E. Kahn and J. B. Thomas, “Bandwidth properties and optimum demodulation of Single-Sideband FM”, IEEE Transactions on Communications Technology, Vol. 14, No.2, April 1966, pp. 113-117.
  7. H. B. Voelcker, “Toward a unified theory of modulation-Parts I and II”, Proceedings of the IEEE, Vol. 54,No. 3, March 1966, pp.340-353, 735-755.

Professor Kalet:

Irving Kalet, Eng.Sc.D., has been teaching and working in the area of digital communications in both Israel and the United States for over 25 years. He lives in Israel, and is currently a consultant both in Israel and at Lucent Technologies (formerly AT&T Bell Laboratories) in the United States. He has worked in the area of mobile wireless communications and digital transmission (HDSL and ADSL) over the twisted-pair cable at Bell Laboratories, and in the area of satellite communications at MIT Lincoln Laboratories. Dr. Kalet has published many papers on digital communications and is the author of the chapter on multitone modulation in the recently published book, Sublet and Wavelet Transforms—Design and Applications (Kluwer Academic Publishers). He is currently working on digital modulation techniques and multiple access techniques for both terrestrial and satellite mobile wireless communications systems. He received his Eng.Sc.D. from Columbia University.





I can recall, over the years, my mother advising me on a method best implemented for perfecting time management and memory skills. A navigational tool used to avoid the errors so frequently made through general carelessness and oversight. "Make a list", she would repeat on a daily basis, and be sure to constantly review, add, and eliminate as you progress through the day (week, month or year, for that matter).

"Patent Specifications", 1934 July 5,

page 1

Not long ago, I recall reading about a book regarding checklists in the New York Times Book ReviewThe Checklist Manifesto: How to Get Things Right, by Atul Gawande was on the bestseller list for months. I can not claim to have read it, but after reading reviews of the book, it seems appropriate to mention it here. Mr. Gawande has apparently written how checklists, used in the medical profession, helped eliminate infections in hospital intensive care units. He expands on this idea, indicating that by extension, it can be applied to virtually any profession. Essentially, with the complexities involved in many of our daily lives, something as simple as a checklist can been seen as a reference tool–providing the steps we need to follow, in order to execute our responsibilities effectively and efficiently.

"Patent Specifications", 1934 July 5,

page 2


For decades the aeronautical industry has used basic checklists for the many aspects of flight navigation and aircraft safety. From plane inspection, takeoff, and flight, to landing, and taxiing, these lists assist  pilots where memory is inadequate. Going through this collection, I constantly come upon "checklists" that the Major created. As you can see through some examples here, many of these lists are more than a page long. A few he titled, as in the one seen here called "Patent Specifications." I suppose it is high time for me to admit it, my mother was right. Given Major Armstrong’s lengthly list of accomplishments, making lists appears to be the way to go. A great majority of the Major’s lists are related to his experimental work, but as seen in some examples here, many have "personal" obligations incorporated.

"Checklist", 1936 March 28,

page 1

One can not help but wonder how it is that Armstrong could have possibly retained, through memory only, results of hundreds of experiments executed days on end, spanning the course of decades, without some type of "aid."  Armstrong would have had to remember those experiments that failed in order to perfect that experiment that succeeded. Only through constant attempts, with changes enacted along the way, could he have produced the precise and correct "one" that served to prove his original theory and thus lead to an invention.


"Checklist", 1936 March 28,

page 2

While I have found quite a  variety of Armstrong’s "to-do" lists, I have to believe that there are quite of number of them that went missing throughout his lengthly career. I would imagine that if all had been preserved, we would perhaps have an even

better idea of how he applied his ideas to the experiments that he developed. He was notorious for not leaving written accounts of this work. For obvious reasons, he was a bit secretive when undertaking experiments. Constantly having to fight for the right to claim his own inventions, it is not a surprise that these discoveries were kept to himself. I hope that these "checklists" will help shed light on a least a portion of the Major’s life and daily activities. You will notice in the lists I have posted here, many of his "goals" are either crossed out, or checked off. Where there are items left unchecked or without a line through it (usually very few), should we infer he never in fact carried out that particular task? Perhaps instead, we should infer that he ran out of time that day.  I, for one, can not fathom that the Major forgot anything….

"Checklist", 1939 November 20


The Regenerative Circuit

Listening to the radio now, as I do quite often, I never would have imagined the difficulties that plagued it in the past. Although not yet around to experience early radio listening first hand, I have read enough to understand just how close one would have had to have been to the speaker. In fact, headphones were generally required. It was here at Columbia University during his undergraduate study that Armstrong made his first momentous discovery, the regenerative circuit, eliminating the need for headphones and providing the foundation of many radio receivers that followed.


Improved Audion Receiver, 1914 January 14

Improved Audion Receiver, 1914 January 14
In 1906, Lee de Forest created the "audion," an early vacuum tube. He had added a third element, the grid, to the Edison-Fleming diode. Subsequently, in 1912, he accidentally connected the output circuit of one audion to its own input circuit and obtained a loud howling sound,which he later identified as regeneration. But instead of attempting to understand this hissing or howling sound, he tried to abolish it.  A modern day example of this phenomenon results when a microphone is placed too close to its accompanying speaker, resulting in an uncomfortable noise (feedback).
When Armstrong began experimenting with the audion, he took numerous measurements in order to figure out how this tube functioned, eventually devising a circuit that would operate as a powerful amplifier of  incoming radio waves (E. H. Armstrong drawing above on left). He figured out that if part of the plates output current was fed back to the grid in a controlled manner, the incoming signals were remarkably strengthened . In addition, he discovered that when feedback was increased sufficiently the circuit could be used as a transmitter by generating high frequency oscillations, a required element for radio communications (E. H. Armstrong drawing below).

Circuits for Using the Audion as a Generator of High Frequency Oscillations, 1914 March 13

Circuits for Using the Audion as a Generator of High Frequency Oscillation, 1914 March 13
Armstrong’s invention led to a nearly twenty-year legal battle over patent rights. Between 1914 and 1934, he and de Forest fought in court both individually and through the corporations (Westinghouse Electric and American Telephone and Telegraph, respectively) who had purchased rights to their patents. Long and complicated, the battle began when de Forest sat in the audience listening to one of Armstrong’s lectures on the transmitting and receiving properties of his regenerative circuit. Although de Forest had given lectures in 1913 on the qualities of his audion invention, he never claimed it retained any of the capacities that Armstrong had discovered.  de Forest went on to submit a claim to the same invention in 1914, but the courts upheld Armstrong as the patent owner for the next ten years. It ended in 1934 when the Supreme Court decided in de Forest’s favor.
Regardless of the Supreme Court’s decision, the engineering community still recognizes Armstrong as the rightful inventor and has given him multiple awards for it. In 1917, the Institute of Radio Engineers (IRE) awarded him their Medal of Honor and in 1942, the American Institute of Electrical Engineers (AIEE) awarded him the Edison Medal, the highest award of the Institute (In 1963, the IRE and the AIEE merged to form the IEEE (Institute of Electrical and Electronics Engineers). These prestigious awards still stand today.
The original early drawings seen here, along with extensive litigation files, can be found within the Edwin H. Armstrong collection.

Vacuum Tube?

A vacuum tube from the Armstrong collection

Most people today have heard of Moore’s Law and the explosion of the number of transistors in modern technology, but if you are of the younger generation, the word “vacuum tube” sparks only faint recognition.  In fact, some younger readers may not recognize the term at all.  But this device was the forerunner of the modern transistor, which is used in nearly all electronics today.

Edison discovered the principle that would lead to the vacuum tube while developing a carbon-filament electric lamp.  In 1883, during the course of his experiments he observed a dark film on the inside of the glass which caused the carbon filament to burn out. Curious as to the cause, Edison hung a tiny metal plate inside the bulb and found that a small current passed from the hot filament to the metal plate, but not in the other direction.

This “Edison phenomenon” was regarded as an academic curiosity for many years, until it was picked up by John Fleming in 1904.  Fleming used this discovery to create the “Fleming valve,” a device that would induce current flow in one direction and not the other.  This is called the “diode” today (a term that many will remember from Physics class).

Closeup of the inside of a vacuum tube

In 1906 Lee De Forest found that he could place a fine wire mesh between the filament and the metal plate and control the current flow through the circuit.  In effect, he made a “faucet”; if the voltage on the grid was high, current would flow.  If the voltage on the grid was low, the current would be blocked.

Think of this as a faucet: by using a little bit of your own energy to turn the knob, you can control a large flow of water.  Similarly, the De Forest “audion,” or vacuum tube used a small voltage from an incoming radio signal to shape a large amount of current provided locally.

You can see a picture of a vacuum tube from the E.H. Armstrong collection at the right.  The wire running through the center is the cathode, the wire spiral is the mesh, and the thick black outer shell is the anode.  This vacuum tube was originally used in the litigation case Armstrong vs. Motorola.

Next, I’ve included a picture of an interesting device below.  Do you recognize it?

Fundamental electronic element


This is a air variable capacitor.  By rotating the plates outwards, the surface area is decreased and the capacitance drops.

Welcome to the Major Armstrong blog

W.H. Lighty's letter of admiration stems from his lengthy career at the University of Wisconsin...continued    

This significant and historically rich collection has been open for use here now for many years. To any who may have searched within it, this will come as some welcome news: thanks to the Armstrong Memorial Research Foundation and generous grants from the IEEE Foundation, the IEEE Communications Society, the IEEE Circuits and Systems Society, Alcatel-Lucent Foundation, Columbia University’s Department of Electrical Engineering, and Fu Foundation School of Engineering and Applied Science, I have been charged with re-processing this collection with the goal of increasing accessibility through the provision of a more descriptive aid.

This blog will highlight just a sliver of this incredible collection. I have been blessed with the luxury of hiring a graduate student, Jen Howard (EE GS ’10), who will be sharing these finds as well (expect forthcoming posts from her!). She is studying for her masters in electrical engineering here, which when contrasted with my humanities background, will serve to provide a broader and hopefully, a more interesting and varied perspective.

On the Title…

By now, you have noticed the letter up on your left—While debating the title of this blog Jen, who has been given the task of researching and describing the photographs, came upon the one shown below of Major Armstrong and William H. Lighty. She pointed out the accompanying letter which we both agreed was perfect—“scientist, technologist, philosopher, inventor triumphant in the arts of communication”.

E.H. Armstrong and W.H. Lighty, WHA Radio Institute, University of Wisconsin, Summer Session, 1945    
E.H. Armstrong and W.H. Lighty, WHA Radio Institute, University of Wisconsin, Summer Session, 1945

The awe and inspiration Lighty expressed in this letter permeated the entire scientific community from the time of Howard’s first creation, the regenerative circuit in 1912 to his complete Frequency Modulation system, in 1933.

 Letter to the Major 1945 August 25     
1945 August 25 Letter to the Major

Edwin Howard Armstrong (known to his friends as Major) is credited with a multitude of inventions in the radio communications field. He secured 42 patents throughout his career, of which the most well known are the regenerative circuit, superheterodyne circuit in 1918, the superregenerative circuit in 1922, and his commercially viable FM Radio system.

Armstrong was of a stubborn character, refusing to follow the accepted mathematical theories of the time. His persistence and systematic method of experimentation produced discoveries that would turn accepted dogma on its head. His creative genius ushered mankind into a new world and his inventions remain the mainstay of wireless communications today.

An invitation…

It is our hope that this blog will serve as not only a place where we can post our finds, but in addition, serve as an informal exchange of information, inspiration, and opinions on this creative genius who was once known as a fixture here at Columbia. He was usually found toiling away in the Marcellus Hartley Laboratory located in the basement of Philosophy Hall. He forms not only a fundamental part of American History, but also a salient part of Columbia University’s history and its renowned engineering school (

I wish to invite and encourage students, faculty, staff, electrical engineers, young radio enthusiasts and historians of Radio History, to post here and pass this site around. Let’s increase interest in this historically rich collection, and the overlooked importance of Armstrong’s role in revolutionizing radio communications.

More posts to follow!


(From first picture caption)

Lighty worked in the field of adult education serving on the administrative staff of the Extension Division and first program manager of Station WHA.  His primary influence was the use of radio broadcast as an educational medium.  WHA is today considered the most successful model  of educational radio in broadcasting history.