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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. RochelleGoddard Space Flight Center Greenbelt,Maryland

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION

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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

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 TELEMETRYby Robert W. Rochelle Goddard Space Flight Center

SUMMARY

This report is concernedwiththeheuristicdevelopment of thebasic features of pulse-frequencymodulation,aninformationencodingtechnique which has been used in a number of spacecraft. The primary advantages are its noise-immunity characteristics and its ease of generation. A description of the present method of formating and synchronization is presented in order to illustrate the convenient handling of both analog and digital data. The theory of group-codedbinary sequences is derived by using a special type of correlation matrix. By combining particular sequences from a number of these correlation matrices, a new matrix is generated which is identical to the correlation matrix of a set of pulse-frequency modulation words. Thus, it is shown that pulse-frequency modulation has the same communication efficiency as a comparable set of coded binary sequences with an equal number of quantized levels. In the detection process for P F M signals, a set of contiguous unmatched filters is used to enhance the signal-to-noise ratio. To examine the effects of Rayleigh noise on the output of these filters, the word-error probability is derived as a function of the energy per bit, noise power density, and degree of coding. The same development is given for the matched-filter case. The analysis of the excitation of an unmatched filter to a step sinusoid is carried out to indicate the magnitude of the e r r o r s affecting the direct frequency measurement of the pulsed sine wave. The analysis also covers the action of a pulsed sine wave in which the frequency is changing as it passes through the filter. Experimental results from the spectral analyses of satellite recordings perturbed with random noise are presented to illustrate the noise-immunity characteristic of pulse-frequency modulation.

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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

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

CONTENTS Summary

................................. INTRODUCTION ............................ The Encoding Problem .....................History of Coded Telemetry CHARACTERISTICS OF PULSE-FREQUENCY MODULATION

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........................... General Description ....................... DesignConsiderations ........................7 1011 Group Coding . . . . . . . . . . . . . . . . . . . . . . . . . . . Parity Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . PFM Correlation Table . . . . . . . . . . . . . . . . . . . . .

CHARACTERISTICS OF CODED BINARY SEQUENCES

NOISE ANALYSIS

........................... Unmatched Filter .

. . . . . . . . . . . . . . . . . . . . . . . Matched Filter . . . . . . . . . . . . . . . . . . . . . . . . . .

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14 2228 30 32 34 34 3841

........ Analysis of Unmatched Filters . . . . . . . . . . . . . . . . Matched-Filter Techniques . . . . . . . . . . . . . . . . . . EXPERIMENTAL RESULTS .................... SpectralAnalysis . . . . . . . . . . . . . . . . . . . . . . . . Signal-to-Noise-RatioComparisons ............ CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ACKNOWLEDGMENTS ........................ References ................................CONTIGUOUS-FILTER DETECTION SYSTEM Appendix A-Amplitude Density Spectrum of a Pulsed Sine Wave

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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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