Ralph V.L. Hartley was inventor of the electronic oscillator circuit that bears his name. He was also a pioneer in the field of Information Theory.

Ralph V.L. Hartley was born in Spruce, Nevada, on 30 November 1888. He graduated with the A.B. degree from the University of Utah in 1909. As a Rhodes Scholar, he received the B.A. degree in 1912 and the B.Sc. degree in 1913 from Oxford University.

Upon returning from England, Hartley joined the Research Laboratory of the Western Electric Company and was given charge of radio-receiver development for the Bell System's transatlantic radiotelephone tests of 1915. He invented his oscillating circuit during that time and also invented a neutralizing circuit to eliminate triode singing resulting from internal coupling.
 

Hartley-oscillator

Linear amplifier with Hartley-oscillator

Hartley oscillator are inductively coupled, variable frequency oscillators where the oscillator may be series or shunt fed. Hartley oscillators have the advantage of having one centre tapped inductor and one tuning capacitor. This arrangement simplifies the construction of a Hartley oscillator circuit.

During World War I, Hartley worked out the principles that led to the development of sound-type directional finders. After the war, he worked at Western Electric and later at the Bell Laboratories, doing research on repeaters, and voice and carrier transmission. During this period he formulated the law "that the total amount of information that can be transmitted is proportional to frequency range transmitted and the time of the transmission."

Hartley was pioneer in the field of Information Theory. He introduced the concept of "information" as random variable and was the first to attempt to define "a measure of information" (1928: "Transmission of Information", in Bell System Tech. Journal, vol. 7, pp. 535-563). Publishing in the same journal as Nyquist, and yet not citing Nyquist (or any one else, for that matter), Hartley developed the concept of information based on "physical as contrasted with psychological considerations" for use in studying electronic communications. In the first section of his paper, titled "The Measurement of Information", he noted that "information is a very elastic term". In fact, Hartley never adequately defines this core concept. Instead, he addresses the "precision of ... information" and the "amount of information". Information exists in the transmission of symbols, with symbols having "certain meanings to the parties communicating". When someone receives information, each received symbol allows the recipient to "eliminate possibilities", excluding other possible symbols and their associated meanings. "The precision of information depends upon what other symbol sequences might have been chosen"; the measure of these other sequences provides an indication of the amount of information transmitted. Nyquist then suggests that we take "as our practical measure of information the logarithm of the number of possible symbol sequences". Thus, if we received 4 different symbols occurring with equal frequency, this would represent 2 bits of information.

It is likely that Hartley was aware of the earlier work of Nyquist and that he assumed implicitly, as Nyquist did explicitly, that all symbol sequences were of the same length or size. The formula Hartley uses is consistent with this assumption, but serves only as an approximation of the information amount if the symbols are of different lengths. Symbols need not be equi-probable for Hartley's formula to be correct if symbols are of equal length. It is probable that Hartley did not make a statement concerning the probability of symbol sequences because of his (implicit) assumption of equal length symbols. Hartley was aware of a relationship between the amount of energy in an information system and the amount of information that could be transmitted. Applying energy to an information transmitting system increases the ease with which the recipient receives or hears the transmitted signal. Energy serves as a component of the transmission process. Increasing the signal to noise ratio increases the probability that the information will be received correctly. Information itself isn't energy carrying; it is energy that carries information.

Possibly his greatest contribution was the creation of a new transform: The Hartley Transform which has many practical applications.
 

In general the Fourier transform is a difficult one to apply because it depends on complex numbers. This problem can be avoided by using a simular, but less used, transform known as the Hartley transform (R.V.L. Hartley, A more symmetrical Fourier analysis applied to transmission problems. Proceedings of the IRE, 30, 144-150, 1942). This transform works entirely in the real number domain and is shown in the following pair of equations.  This transform shares many of properties of the Fourier transform including the Fourier slice theorem. This means that the Hartley transform would make a good replacement for volume rendering purposes. One drawback of using the Hartley transform is that it is difficult to extend to higher dimensions because it is not a separable transform. R. Bracewell introduced a way around this problem through the use of the following trig identity (R.N. Bracewell, O. Buneman, H. Hao, J. Villasenor, Fast two-dimensional Hartley transform. Proceedings of the IEEE, 74, 1282-1283, 1986). This identity allows for the two dimensional Harley transform to be calculated by assuming dimensional independence followed by applying the above equation to correct for the assumption.

Illness kept Hartley away from research for about ten years, but in 1939 he returned to Bell Labs as a consultant, and during World War II he was particularly involved with servo problems. He retired from Bell Labs in 1950.

Hartley was awarded the IRE Medal of Honor in 1946 "for his early work on oscillating circuits employing triode tubes and likewise for his early recognition and clear exposition of the fundamental relationship between the total amount of information which may be transmitted over a transmission system of limited band-width and the time required." He was a Fellow of the American Association for the Advancement of Science. Hartley also contributed with more than 70 patents.

Ralph V.L. Hartley died on 1 May 1970 at the age of 81.