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相关概念视频

Continuous -time Fourier Transform01:11

Continuous -time Fourier Transform

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The Fourier series is instrumental in representing periodic functions, offering a powerful method to decompose such functions into a sum of sinusoids. This technique, however, necessitates modification when applied to nonperiodic functions. Consider a pulse-train waveform consisting of a series of rectangular pulses. When these pulses have a finite period, they can be accurately represented by a Fourier series. Yet, as the period approaches infinity, resulting in a single, isolated pulse, the...
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Properties of Fourier Transform II01:24

Properties of Fourier Transform II

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The Fourier Transform (FT) is an essential mathematical tool in signal processing, transforming a time-domain signal into its frequency-domain representation. This transformation elucidates the relationship between time and frequency domains through several properties, each revealing unique aspects of signal behavior.
The Frequency Shifting property of Fourier Transforms highlights that a shift in the frequency domain corresponds to a phase shift in the time domain. Mathematically, if x(t) has...
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Properties of Fourier Transform I01:21

Properties of Fourier Transform I

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The application of Fourier Transform properties in radio broadcasting is multifaceted, enabling significant advancements in the way signals are transmitted and received. Key areas where these properties are utilized include simultaneous multi-channel transmission, audio clip speed adjustments, live broadcast delays for different time zones, audio frequency adjustments, and signal demodulation.
In radio broadcasting, multiple audio signals often need to be transmitted simultaneously. The Fourier...
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Convergence of Fourier Series01:21

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The Fourier series is a powerful mathematical tool for representing periodic signals as an infinite sum of complex exponentials. In practice, this infinite series is truncated to a finite number of terms, yielding a partial sum. This truncation makes the approximation of the signal feasible but introduces certain challenges, particularly near discontinuities, known as the Gibbs phenomenon.
The Gibbs phenomenon refers to the persistent oscillations and overshoots that occur near discontinuities...
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Uncertainty: Overview00:59

Uncertainty: Overview

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In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.
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Parseval's theorem is a fundamental principle in signal processing that enables the calculation of a signal's energy in either the time domain or the frequency domain. This theorem is pivotal in demonstrating energy conservation between these two domains, ensuring that the computed energy value remains consistent regardless of the domain of analysis.
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相关实验视频

Updated: Sep 16, 2025

Measurement of the Directional Information Flow in fNIRS-Hyperscanning Data using the Partial Wavelet Transform Coherence Method
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不确定性意识的富里埃图形图形学

Ni Chen1, Yang Wu2, Chao Tan2

  • 1Department of Electrical and Electronic Engineering, The University of Hong Kong, Hong Kong SAR, China. nichen@eee.hku.hk.

Light, science & applications
|July 7, 2025
PubMed
概括

不确定性意识里叶图谱 (UA-FP) 同时纠正系统不确定性,以改善全息成像. 这种新的框架可以在没有复杂校准的情况下在具有挑战性的条件下提高重建质量.

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科学领域:

  • 光学和成像科学科学 光学和成像科学
  • 计算成像技术的成像
  • 全息影像的使用方法.

背景情况:

  • 富里埃图谱 (FP) 提供了广的视野和高分辨率成像,但对系统不确定性敏感.
  • 目前的方法单独解决不确定性,如错位和偏差,未能解决相互连接的退化.
  • 挑战包括精确的数值建模,光学偏差和实际FP实施中的数据质量限制.

研究的目的:

  • 引入一个全面的框架,不确定性意识FP (UA-FP),用于同时解决FP中的多个系统不确定性.
  • 开发一个可微分的前模型,将确定性和随机性不确定性作为可优化的参数.
  • 为了实现强大的FP性能,而无需进行广泛的校准或数据收集.

主要方法:

  • 为FP开发了一个完全可分化的前置成像模型.
  • 纳入确定性不确定性 (错位,偏差) 作为可优化的参数.
  • 对于随机不确定性 (噪音,数据质量) 用了具有域特定先验的可分化优化.

主要成果:

  • 在具有挑战性的条件下,UA-FP实现了卓越的重建质量.
  • 证明了强大的性能,降低了子频谱重叠要求.
  • 即使使用低位传感器数据,也保持了高质量的重建.

结论:

  • UA-FP提供了一种统一的方法来缓解FP中相互关联的不确定性.
  • 该框架增强了系统的重新配置性,并扩大了FP在不受控制的环境中的适用性.
  • 这种方法推进FP作为一个强大的测量工具,用于实际的,现实世界的应用.