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Related Concept Videos

Linearization and Approximation01:26

Linearization and Approximation

Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
Application of Linearization and Approximation01:29

Application of Linearization and Approximation

A drone flying through complex terrain often relies on more than one sensing method to estimate small changes in altitude. Along with direct measurements, air pressure provides a useful indirect indicator of vertical movement. Atmospheric pressure decreases as altitude increases, and this relationship is commonly described using an exponential model. Although accurate, converting pressure measurements into altitude values requires calculations that are too complex to perform repeatedly during...
Linear Approximations01:23

Linear Approximations

For a differentiable function of two variables, linear approximation estimates values near a known point by replacing the curved surface with its tangent plane. Consider the function\begin{equation*}f(x,y)=x^2+3y^2\end{equation*}near the point (2, 1). The exact value at this point is f(2, 1) = 22 + 3(1)2 = 4 + 3 = 7.The linear approximation of f(x, y)) near (a, b) is\begin{equation*}L(x,y)=f(a,b)+f_x(a,b)(x-a)+f_y(a,b)(y-b)\end{equation*}First, compute the partial derivatives: fx(x, y) = 2x and...

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Published on: February 12, 2013

Adaptive optical post distortion linearization.

Jason Chou, Ozdal Boyraz, Bahram Jalali

    Optics Express
    |June 6, 2009
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces adaptive optical domain post distortion to suppress optical nonlinearities. The technique effectively cancels unwanted signal components, achieving over 20 dB extinction in four-wave mixing.

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    Published on: February 23, 2017

    Area of Science:

    • Photonics and optical engineering
    • Nonlinear optics
    • Signal processing

    Background:

    • Optical nonlinearities degrade signal quality in optical communication systems.
    • Existing linearization techniques often require complex hardware or are limited in scope.

    Purpose of the Study:

    • To demonstrate a novel technique for suppressing optical nonlinearities using adaptive post-distortion.
    • To mitigate nonlinear effects by generating phase-canceled sidebands.

    Main Methods:

    • Modeling and experimental validation of adaptive optical domain post distortion.
    • Utilizing an adaptive phase controller and computer feedback loop.
    • Generating phase-inverted sidebands to cancel unwanted nonlinear components.

    Main Results:

    • Achieved >20 dB extinction of nonlinear components, specifically in four-wave mixing.
    • Demonstrated the effectiveness of the adaptive phase controller in real-time suppression.
    • Validated the concept of electrical domain linearization principles applied to the optical domain.

    Conclusions:

    • Adaptive optical domain post distortion is a viable method for suppressing optical nonlinearities.
    • The technique offers significant extinction ratios, improving signal integrity.
    • This approach provides a flexible and effective solution for advanced optical systems.