摘要翻译：
本文研究了信号在史瓦西时空中的变化，给出了频移参数(FSP)的一般方程。结果表明，FSP依赖于重力修正的多普勒效应和观测者的重力效应。此外，发射机和接收机的时间速率可以不同。当FSP是接收机时间的函数时，由重力效应(GFSP)或重力修正多普勒效应(GMDFSP)贡献的FSP可能会将带限信号引导到非带限信号。在此基础上，计算了三种情况下FSP随接收机时间的变化：a）宇宙飞船以等速远离恒星，在固定位置与发射机通信；b）宇宙飞船绕不同圆锥曲线轨道的恒星运动，与固定位置的发射机通信；c）在恒星系统的固定位置向另一恒星系统的椭圆轨道的接收机发射信号。研究的恒星有类太阳星、白矮星和中子星，并给出了一些数值例子来说明理论。
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英文标题：
《Variation of a Signal in Schwarzschild Spacetime》
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作者：
Huan Liu, Xiang-Gen Xia and Ran Tao
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最新提交年份：
2019
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分类信息：

一级分类：Electrical Engineering and Systems Science        电气工程与系统科学
二级分类：Signal Processing        信号处理
分类描述：Theory, algorithms, performance analysis and applications of signal and data analysis, including physical modeling, processing, detection and parameter estimation, learning, mining, retrieval, and information extraction. The term "signal" includes speech, audio, sonar, radar, geophysical, physiological, (bio-) medical, image, video, and multimodal natural and man-made signals, including communication signals and data. Topics of interest include: statistical signal processing, spectral estimation and system identification; filter design, adaptive filtering / stochastic learning; (compressive) sampling, sensing, and transform-domain methods including fast algorithms; signal processing for machine learning and machine learning for signal processing applications; in-network and graph signal processing; convex and nonconvex optimization methods for signal processing applications; radar, sonar, and sensor array beamforming and direction finding; communications signal processing; low power, multi-core and system-on-chip signal processing; sensing, communication, analysis and optimization for cyber-physical systems such as power grids and the Internet of Things.
信号和数据分析的理论、算法、性能分析和应用，包括物理建模、处理、检测和参数估计、学习、挖掘、检索和信息提取。“信号”一词包括语音、音频、声纳、雷达、地球物理、生理、（生物）医学、图像、视频和多模态自然和人为信号，包括通信信号和数据。感兴趣的主题包括：统计信号处理、谱估计和系统辨识；滤波器设计；自适应滤波/随机学习；（压缩）采样、传感和变换域方法，包括快速算法；用于机器学习的信号处理和用于信号处理应用的机器学习；网络与图形信号处理；信号处理中的凸和非凸优化方法；雷达、声纳和传感器阵列波束形成和测向；通信信号处理；低功耗、多核、片上系统信号处理；信息物理系统的传感、通信、分析和优化，如电网和物联网。
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英文摘要：
  In this paper, the variation of a signal in Schwarzschild spacetime is studied and a general equation for frequency shift parameter (FSP) is presented. It shows that FSP depends on the gravitationally-modified Doppler effects and the gravitational effects of observers. In addition, rates of time of a transmitter and a receiver may be different. When FSP is a function of the time of a receiver, FSP contributed by gravitational effect (GFSP) or gravitationally-modified Doppler effect (GMDFSP) may lead a bandlimited signal to a non-bandlimited signal. Based on the equation, FSP as a function of the time of a receiver is calculated for three scenarios: a) a spaceship moves away from a star with a constant velocity communicating with a transmitter at a fixed position; b) a spaceship moves around a star with different conic trajectories communicating with a transmitter at a fixed position; c) a signal is transmitted at a fixed position in a star system to a receiver moving with an elliptical trajectory in another star system. The studied stars are sun-like star, white dwarf and neutron star, and some numerical examples are presented to illustrate the theory.
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PDF链接：
https://arxiv.org/pdf/1807.08914