title: ÐÐ·Ð¼ÐµÑÐ¸ÑÐµÐ»Ñ Ð½Ð°ÑÐ°Ð»ÑÐ½Ð¾Ð¹ ÑÐ°Ð·Ñ Ð·Ð°ÑÑÐ¼Ð»ÐµÐ½Ð½Ð¾Ð³Ð¾ Ð³Ð°ÑÐ¼Ð¾Ð½Ð¸ÑÐµÑÐºÐ¾Ð³Ð¾ ÑÐ¸Ð³Ð½Ð°Ð»Ð° Ð¿ÑÐ¸ ÑÐ°ÑÑÐ¾ÑÐµ Ð¾ÑÑÑÐµÑÐ¾Ð² Ð½Ð¸Ð¶Ðµ ÑÐ°ÑÑÐ¾ÑÑ ÐÐ°Ð¹ÐºÐ²Ð¸ÑÑÐ°
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Measurement of the initial phase of a noisy harmonic signal at a sampling frequency less than the Nyquist frequency
Creators: name: ÐÐ¾ÑÐºÐ¸Ð½Ð°, ÐÐ»ÑÐ±Ð¸Ð½Ð°
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2024
Subjects: Ð¿ÐµÐ»ÐµÐ½Ð³Ð°ÑÐ¸Ñ
Ð½Ð°ÑÐ°Ð»ÑÐ½Ð°Ñ ÑÐ°Ð·Ð° Ð·Ð°ÑÑÐ¼Ð»ÐµÐ½Ð½Ð¾Ð³Ð¾ Ð³Ð°ÑÐ¼Ð¾Ð½Ð¸ÑÐµÑÐºÐ¾Ð³Ð¾ ÑÐ¸Ð³Ð½Ð°Ð»Ð°
Ð¼ÐµÑÐ¾Ð´ Ð¿Ð¾ÐºÐ¾Ð¾ÑÐ´Ð¸Ð½Ð°ÑÐ½Ð¾Ð³Ð¾ ÑÐ¿ÑÑÐºÐ°
Ð¿ÑÐµÐ¾Ð±ÑÐ°Ð·Ð¾Ð²Ð°Ð½Ð¸Ðµ ÐÐ¸Ð»ÑÐ±ÐµÑÑÐ°
Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼ ÐÐ¾ÑÐ¾Ð½Ð¾Ð²Ð°
C
Gnuplot
Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ðµ ÑÐ°Ð·Ñ ÑÐ¸Ð³Ð½Ð°Ð»Ð°
ARM
direction finding
initial phase of a noisy harmonic signal
coordinate descent method
Hilbert transform
Voronovs algorithm
signal phase determination

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description: An algorithm for measuring the initial phase of a noisy harmonic signal was presented at a sampling frequency less than the Nyquist frequency. This work is dedicated to the exploration of various methods for determining the initial phase of a noisy harmonic signal and the development of a program in C language, implementing the algorithm of the original method, and allowing its hardware implementation on the ARM processor, included in the Xilinx ZYNG-7000 SoC FPGA. Tasks addressed during the research: 1. Study methods for determining the initial phase of a noisy harmonic signal. 2. Analyze the original algorithm for measuring the initial phase of a noisy harmonic signal with a sampling frequency below the Nyquist frequency. 3. Implement and simulate the operation of the main algorithm blocks, including the optimization module, in C/C++. 4. Investigate the achievable accuracy of determining the initial phase of a harmonic signal with noise standard deviation ranging from 0.1 to 0.2 with a unit amplitude of the original harmonic signal. 5. Conduct experimental research of the developed system. 6. Describe the possible implementation of the developed program on the ARM processor, included in the Xilinx ZYNG-7000 SoC FPGA. As a result, methods for determining the initial phase of a harmonic signal were analyzed, including the original one. A refinement of the method was proposed using optimization by the coordinate descent method. The algorithm of the method with refinement was implemented and simulated, and the achievable accuracy of determining the initial phase of a harmonic signal was investigated for noise standard deviation ranging from 0.1 to 0.2 with a unit amplitude of the original harmonic signal, as well as other measurements and comparison with the original algorithm. Additionally, the implementation of the resulting program on the ARM processor included in the FPGA Xilinx ZYNQ-7000 SoC is described and the result of running this program is presented. The developed program demonstrates better results in calculating the absolute error of phase determination in degrees and can be used in various fields related to bearing determination.