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Related Concept Videos

Transfer Function to State Space01:23

Transfer Function to State Space

797
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...
797
State Space to Transfer Function01:21

State Space to Transfer Function

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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:
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Transfer function and Bode Plots-II01:23

Transfer function and Bode Plots-II

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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:
749
Transfer function and Bode Plots-I01:19

Transfer function and Bode Plots-I

733
A transfer function presented in its standard form integrates elements' constant gain, the zeros, and poles at the origin, simple zeros and poles, and quadratic poles and zeros. The transfer function can be written as H(ω):
733
Transfer Function in Control Systems01:21

Transfer Function in Control Systems

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The transfer function is a fundamental concept in the analysis and design of linear time-invariant (LTI) systems. It offers a concise way to understand how a system responds to different inputs in the frequency domain. It serves as a bridge between the time-domain differential equations that describe system dynamics and the frequency-domain representation that facilitates easier manipulation and analysis.
To derive the transfer function, consider a general nth-order linear time-invariant...
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Exponential Functions with Base e01:30

Exponential Functions with Base e

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Exponential functions with base e are essential for modeling continuous processes of growth and decay. The constant e, approximately 2.718, naturally arises in systems where change occurs proportionally to the current value. A positive exponent represents continuous growth, while a negative exponent represents continuous decay. These functions are especially useful for describing situations where change happens smoothly over time rather than in discrete steps.One clear example of exponential...
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Related Experiment Video

Updated: Jan 30, 2026

Modulating Shape of Polyester Based Polymersomes using Osmotic Pressure
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Practical edge-based modulation transfer function measurement.

Kenichiro Masaoka

    Optics Express
    |January 31, 2019
    PubMed
    Summary

    This study enhances modulation transfer function (MTF) measurement accuracy in sampled imaging systems by selecting optimal binning phases. A novel method approximates the fundamental MTF without edge angle estimation or subpixel binning, improving precision for various edge types.

    Area of Science:

    • Image processing
    • Optical metrology
    • Quantitative imaging

    Background:

    • The modulation transfer function (MTF) is crucial for evaluating sampled imaging system performance.
    • Subpixel binning in edge-based MTF methods introduces shift-variance, affecting accuracy and precision.
    • Existing methods often require complex edge angle estimation and subpixel binning.

    Purpose of the Study:

    • To develop a more accurate and precise method for measuring the MTF of sampled imaging systems.
    • To overcome the limitations imposed by subpixel binning and edge angle estimation.
    • To propose an algorithm applicable to various edge types, including oblique and non-straight edges.

    Main Methods:

    • A novel algorithm is proposed that averages aliased MTFs from row-by-row edge gradients.

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  • The method removes an assumed aliasing component to approximate the non-aliased, fundamental MTF.
  • This approach avoids explicit edge angle estimation and subpixel binning.

    • Main Results:

    • A practical precision criterion for MTF measurement can be achieved by selecting an appropriate binning phase.
    • The proposed method successfully approximates the fundamental MTF without requiring edge angle estimation.
    • The algorithm demonstrates applicability to both straight and non-straight edges.

    Conclusions:

    • The developed method offers improved accuracy and precision for MTF measurements in sampled imaging systems.
    • The technique simplifies MTF calculation by eliminating the need for edge angle estimation and subpixel binning.
    • This approach provides a robust solution for MTF assessment across diverse imaging scenarios.