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Related Concept Videos

Transfer Function to State Space01:23

Transfer Function to State Space

795
State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
In an RLC...
795
State Space to Transfer Function01:21

State Space to Transfer Function

576
The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:
576
Nonlinear Pharmacokinetics: Causes of Nonlinearity01:22

Nonlinear Pharmacokinetics: Causes of Nonlinearity

718
Nonlinearity in drug pharmacokinetics is caused by various factors influencing how a drug is absorbed, distributed, metabolized, and excreted. Understanding these nonlinear processes is crucial for predicting drug behavior in the body and optimizing drug dosing regimens.
Nonlinear drug absorption can occur when the process is rate-limited by solubility, carrier-mediated transport systems, or saturation of the presystemic gut wall or hepatic metabolism. For instance, high doses of riboflavin...
718
Time and frequency -Domain Interpretation of Phase-lead Control01:24

Time and frequency -Domain Interpretation of Phase-lead Control

446
Phase-lead controllers are commonly used in various control systems to enhance response speed and stability. Adjusting the brightness on a television screen offers a practical example of phase-lead control. When contrast is enhanced, a phase-lead controller is employed. Mathematically, phase-lead control is identified when the first parameter is smaller than the second.
The design of phase-lead control involves the strategic placement of poles and zeros to balance steady-state error and system...
446
Time and frequency -Domain Interpretation of Phase-lag Control01:21

Time and frequency -Domain Interpretation of Phase-lag Control

414
Phase-lag controllers are widely used in control systems to improve stability and reduce steady-state errors. A dimmer switch controlling the brightness of a light bulb serves as a practical example of phase-lag control, gradually adjusting the bulb's brightness. Mathematically, phase-lag control or low-pass filtering is represented when the factor 'a' is less than 1.
Phase-lag controllers do not place a pole at zero, but instead influence the steady-state error by amplifying any...
414
Transfer function and Bode Plots-II01:23

Transfer function and Bode Plots-II

745
In the standard form, the transfer function is shown in constant gain, poles/zeros at origin, simple poles/zeros, and quadratic poles/zeros; each contributing uniquely to the system's overall response. The term represents the magnitude of the simple zero:
745

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Related Experiment Video

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Three-Dimensional Phase Resolved Functional Lung Magnetic Resonance Imaging
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Design of nonlinearly spaced phase-shifting algorithms using their frequency transfer function.

Manuel Servin, Moises Padilla, Guillermo Garnica

    Applied Optics
    |March 16, 2019
    PubMed
    Summary

    This study introduces a new method for designing phase-shifting algorithms (PSAs) for nonlinear phase shifts. The frequency transfer function (FTF) approach allows for precise control and noise reduction in fringe pattern analysis.

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    Area of Science:

    • Optical metrology
    • Image processing
    • Interferometry

    Background:

    • Phase-shifting algorithms (PSAs) are crucial for quantitative analysis of fringe patterns in optical metrology.
    • Standard PSAs assume linear phase steps, limiting their application in scenarios with nonlinear or nonuniform phase shifts.
    • Nonlinear phase shifts can arise from various sources, including system aberrations and environmental factors, complicating fringe analysis.

    Purpose of the Study:

    • To develop a systematic method for designing phase-shifting algorithms (PSAs) tailored for nonuniform/nonlinear (NL) phase-shifted fringe patterns.
    • To leverage the frequency transfer function (FTF) for designing NL-PSAs.
    • To enhance the robustness and accuracy of fringe analysis in the presence of nonlinear phase shifts and noise.

    Main Methods:

    • Designing phase-shifting algorithms (PSAs) by manipulating the frequency transfer function (FTF).
    • Introducing specific zeroes into the FTF to derive tailored nonlinear (NL) PSA formulas.
    • Utilizing the FTF to reject distorting harmonics present in fringe patterns.
    • Estimating the signal-to-noise ratio (SNR) for interferograms affected by additive white Gaussian noise.

    Main Results:

    • A novel method for designing NL-PSAs based on their FTF is presented.
    • The FTF-based design allows for effective rejection of distorting harmonics in fringe patterns.
    • The proposed NL-PSA accurately retrieves the modulating phase error for non-distorted, noiseless fringes, comparable to standard linear PSAs.
    • The method provides a means to estimate SNR in noisy interferograms.

    Conclusions:

    • The FTF provides a powerful framework for designing effective NL-PSAs.
    • The developed NL-PSAs offer improved accuracy and noise resilience for fringe pattern analysis.
    • This approach broadens the applicability of phase-shifting techniques to more complex optical measurement scenarios.