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Appendix B-Autocorrelation Function for Gaussian Noise Appendix C-Response of a Single-Pole Filter to a Step Sinusoid Appendix D-Response of a Single-Pole Filter to a ChangingFrequency
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This report is concerned with the heuristic development of the basic features of pulse-frequency modulation, an information encoding technique which has been used in a number of spacecraft. The primary advantages are its noise-immunity characteristics and
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This report is concerned with the heuristic development of the basic features of pulse-frequency modulation, an information encoding technique which has been used in a number of spacecraft. The primary advantages are its noise-immunity characteristics and
PULSE-FREQUENCY-MODULATION TELEMETRY *by Robert W. Rochelle Goddard Space Flight Center
INTRODUCTIONThe problem of communicating over large distances with minimum power is particularly challenging in view of the advances in information theory during the last 2 decades. With this theory as a guide, a number of interesting types of communication systems can be postulated which, in the limit, approach the theoretical maximum communication efficiency. The encoding methods of some of these systems are exceedingly complex in their implementation. The ideal type of system retains a high communication efficiency with little loss in simplicity. Pulse-frequency modulation is an attempt to fulfill these two basic criteria. Pulse-frequency modulation (PFM) has been successfully employed as the information encoding technique in a number of small (< 200 lb) scientific satellites and space probes where the reduction of spacecraft power and weight was a prime consideration. The use of such systems leaves a greater percentage of the spacecraft available for scientific instrumentation. Since little information has appeared in the literature on the subject, it is hoped that this work will provide a background f o r practical usage, as well as a theoretical derivation, of pulse-frequency modulation.
The EncodingProblemTelemetry implies measurement at a distance. The concept of modern telemetry includes the gathering and encoding of information at a remote station, transmitting this encoded signal to the receiving station, decoding the signal at this station, and presenting the measurements in an acceptable form. The transmission path may involve propagation by radio, light, o r even sound waves. Attenuation of the transmitted signal is usually a predominant factor because of the physical separation between the transmitting and receiving apparatus. If attenuation is low, the choices of the encoding and modulation methods are not critical, and methods which lead to simple and reliable sy
stems are usually employed. With the introduction of attenuation in the transmission path, interference in various forms may perturb the signals and cause transmission errors. By proper encoding of the information, the effect of these noise perturbations can be minimized. The amount of
*This report was submitted to the University of Maryland a s partial fulfillment of the requirements for rhe degree of Doctor of Philosophy.
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This report is concerned with the heuristic development of the basic features of pulse-frequency modulation, an information encoding technique which has been used in a number of spacecraft. The primary advantages are its noise-immunity characteristics and
improvement or immunization to noise that can be accomplishedis governed by Shannon's channel capacity theorem (Reference 1):
where c is the channel capacity (bits per second), B is the channel bandwidth, P is the signal power, and N is the average noise power. As the signal power is decreased, the bandwidth of the encoded signal must be increased to maintain the same channel capacity and probability of error. Various schemes can be devised to take advantage Shannon's channel capacity theorem and of thereby reduce the transmitter power for a given information rate. Kotel'nikov has described the general theory of high efficiency encoding (Reference 2). The problem involved is to approach the Shannon channel-capacity limit as closely as possible. But this must be consistent with the ability to implement the encoding scheme with equipment which is not of undue complexity. A practical example of this problem is the telemetering of scientific data from satellites and space probes. Since spacecraft power is limited, savings in transmitter power due to efficientcoding can extend either the range or information rate or both. The improvement is greater in the small satellite class (< 2001b), where a larger percentage of the satellite weight is devoted to the transmitter power system.
History of Coded TelemetryCoded telemetry began with the early work on frequency modulation. At that time frequency modulation was thought to require less bandwidth than amplitude modulation, since the frequency deviation could be made smaller than the modulating frequency. Carson disproved this theory in 1922 (Reference 3). In 1936 Armstrong demonstrated the major advantage of frequency modulation-the improvement of the signal-to-noise ratio for large frequency deviations (Reference 4). The system traded bandwidth for signal-to-noise-ratio improvement. A recognized deficiency was the sharp threshold or decrease in the signal-to-noise ratio at low signal levels. Pulse-code modulation* developed much more slowly than frequency modulation (Reference 5). It was not until 1948 that Shannon predicted that pulse-code modulation would have error-reducing properties (Reference 1). In 1950 Hamming devised a practical scheme of coding to effect these error-reducing properties (Reference 6). He introduced the error-detecting parity bit for a binary sequence and added bits to these for error-correcting purposes. Since 1950, numerous papers have been written on the subject of coding theory. Viterbi utilized these theories in calculating error probability as a
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