摘要翻译：
信号缩放是在坐标方向上放大或缩小信号的一种具有实际意义的基本操作。对于离散变量的信号来说，缩放或放大并不简单，因为信号值可能不落在离散坐标点上。一种方法是将离散间隔的值视为实变量信号的样本，通过插值找到该信号，对其进行缩放，然后重新采样。然而，这种方法伴随着解释的复杂性。我们回顾了以前提出的另一种更优雅的方法，然后提出了一种基于超微分算子理论的新方法，我们发现它在获得与离散傅立叶变换理论完全一致的自洽、纯和优雅的离散标度定义方面是最令人满意的。
---
英文标题：
《Discrete Scaling Based on Operator Theory》
---
作者：
Aykut Ko\c{c}, Burak Bartan, Haldun M. Ozaktas
---
最新提交年份：
2018
---
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。
--

---
英文摘要：
  Signal scaling is a fundamental operation of practical importance in which a signal is enlarged or shrunk in the coordinate direction(s). Scaling or magnification is not trivial for signals of a discrete variable since the signal values may not fall onto the discrete coordinate points. One approach is to consider the discretely-spaced values as the samples of a signal of a real variable, find that signal by interpolation, scale it, and then re-sample. However, this approach comes with complications of interpretation. We review a previously proposed alternative and more elegant approach, and then propose a new approach based on hyperdifferential operator theory that we find most satisfactory in terms of obtaining a self-consistent, pure, and elegant definition of discrete scaling that is fully consistent with the theory of the discrete Fourier transform.
---
PDF链接：
https://arxiv.org/pdf/1805.035