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相关概念视频

Inverse z-Transform by Partial Fraction Expansion01:20

Inverse z-Transform by Partial Fraction Expansion

308
The inverse z-transform is a crucial technique for converting a function from its z-domain representation back to the time domain. One effective method for finding the inverse z-transform is the Partial Fraction Method, which involves decomposing a function into simpler fractions with distinct coefficients. These fractions correspond to known z-transform pairs, facilitating the inverse transformation process.
To begin the process, the poles of the function are identified and the function is...
308
Difference Equation Solution using z-Transform01:24

Difference Equation Solution using z-Transform

271
The z-transform is a powerful tool for analyzing practical discrete-time systems, often represented by linear difference equations. Solving a higher-order difference equation requires knowledge of the input signal and the initial conditions up to one term less than the order of the equation.
The z-transform facilitates handling delayed signals by shifting the signal in the z-domain, which corresponds to delaying the signal in the time domain, and advancing signals by similarly shifting in the...
271
Focusing of Light in the Eye01:16

Focusing of Light in the Eye

2.6K
Light rays enter the eye through the cornea, a transparent dome-shaped tissue that is the eye's outermost layer. The cornea bends or refracts, light rays traveling to the pupil. The shape of the cornea determines how much of the light is bent and whether the image will be focused correctly on the retina at the back of the eye. Once the light has passed through both refraction layers, it converges into a single focal point onto a small area. This is where photoreceptors start transforming...
2.6K
Properties of the z-Transform II01:16

Properties of the z-Transform II

111
The property of Accumulation in signal processing is derived by analyzing the accumulated sum of a discrete-time signal and using the time-shifting property to determine its z-transform. This principle reveals that the z-transform of the summed signal is related to the z-transform of the original signal by a multiplicative factor.
Moreover, the convolution property indicates that the convolution of two signals in the time domain corresponds to the product of their z-transforms in the frequency...
111
Properties of the z-Transform I01:17

Properties of the z-Transform I

173
The z-transform is a fundamental tool in digital signal processing, enabling the analysis of discrete-time systems through its various properties. It is an invaluable tool for analyzing discrete-time systems, offering a range of properties that simplify complex signal manipulations. One fundamental property is linearity. For any two discrete-time signals, the z-transform of their linear combination equals the same linear combination of their individual z-transforms. This property is essential...
173
Definition of z-Transform01:26

Definition of z-Transform

415
The z-transform is a powerful mathematical tool used in the analysis of discrete-time signals and systems. It is an essential analytical tool, analogous to the Laplace transform used in continuous-time systems. It plays a crucial role in the analysis of signals and systems, complementing the discrete-time Fourier transform. Both the z-transform and the Laplace transform convert differential or difference equations into algebraic equations, simplifying the process of solving complex problems.
415

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相关实验视频

Updated: Jun 16, 2025

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture
09:04

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture

Published on: February 23, 2018

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通过泽尼克多项式优化渐进加法镜头.

Yuechen Shen, Yunhai Tang, Quanying Wu

    Optics express
    |June 14, 2025
    PubMed
    概括

    本研究介绍了一种使用Zernike多项式和分析层次过程 (AHP) 优化渐进加法镜头 (PALs) 的高效方法. 这种新方法显著减少了计算时间,并提高了镜头性能.

    科学领域:

    • 光学和光子学 在光学和光子学.
    • 计算设计的计算设计.
    • 眼科镜片技术 眼科镜片技术

    背景情况:

    • 传统上,对渐进式加法镜头 (PAL) 表面的高精度建模需要大量的泽尼克多项式 (231),从而带来了重大的计算挑战.
    • 对于PALs,现有的优化方法可能是计算密集型和耗时的,阻碍了快速的设计代和制造.

    研究的目的:

    • 开发一种创新且计算效率高的方法来优化渐进加法镜头 (PAL) 表面.
    • 通过改善远视和近视区域的宽度来提高PALs的性能.
    • 为了减少PAL表面优化所需的计算时间.

    主要方法:

    • 在PAL表面建模的商业光学设计软件中利用Zernike多项式系数.
    • 采用分析层次流程 (AHP) 在优点函数内系统地分配权重.
    • 引入了一种新的技术,以最大限度地减少优化变量的数量,从而提高效率.

    主要成果:

    • 与传统优化方法相比,计算时间减少了79.6%.
    • 在制造镜片样本中,远视区的宽度增加了17.2%.
    • 在制造镜片样本中,近视区的宽度增加了15.9%.

    更多相关视频

    Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
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    Lensfree On-chip Tomographic Microscopy Employing Multi-angle Illumination and Pixel Super-resolution
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    Lensfree On-chip Tomographic Microscopy Employing Multi-angle Illumination and Pixel Super-resolution

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    Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture
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    Published on: February 23, 2018

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    Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
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    Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

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    Lensfree On-chip Tomographic Microscopy Employing Multi-angle Illumination and Pixel Super-resolution
    08:41

    Lensfree On-chip Tomographic Microscopy Employing Multi-angle Illumination and Pixel Super-resolution

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    结论:

    • 拟议的方法为PAL优化的计算效率提供了显著的改进.
    • 优化的PAL显示器具有更广泛的距离和近距离视觉区域的增强视觉性能.
    • 这种方法为设计和制造先进的渐进式添加镜头提供了有效的策略.