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Related Concept Videos

Transfer Function in Control Systems01:21

Transfer Function in Control Systems

1.9K
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...
1.9K
Transfer function and Bode Plots-II01:23

Transfer function and Bode Plots-II

1.0K
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:
1.0K
Network Function of a Circuit01:25

Network Function of a Circuit

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Frequency response analysis in electrical circuits provides vital insights into a circuit's behavior as the frequency of the input signal changes. The transfer function, a mathematical tool, is instrumental in understanding this behavior. It defines the relationship between phasor output and input and comes in four types: voltage gain, current gain, transfer impedance, and transfer admittance. The critical components of the transfer function are the poles and zeros.
1.0K
Transfer function and Bode Plots-I01:19

Transfer function and Bode Plots-I

1.0K
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):
1.0K
State Space to Transfer Function01:21

State Space to Transfer Function

684
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:
684
Transfer Function to State Space01:23

Transfer Function to State Space

961
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...
961

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Updated: Apr 10, 2026

Transient Optical Clearing Using Absorbing Molecules for Ex Vivo and In Vivo Imaging
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Visualization and quality assessment of the contrast transfer function estimation.

Lisa K Sheth1, Angela L Piotrowski1, Neil R Voss1

  • 1Roosevelt University, Department of Biological, Chemical, and Physical Sciences, 1400 N. Roosevelt Blvd., Schaumburg, IL 60173, USA.

Journal of Structural Biology
|June 17, 2015
PubMed
Summary

Transmission electron microscopy users can now better assess image quality using a new graphical output and CTF resolution metric. These tools simplify contrast transfer function (CTF) parameter selection for improved data processing.

Keywords:
Computer-assisted image processingContrast transfer functionCryo-electron microscopy methodsTransmission electron microscopy

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Area of Science:

  • Microscopy
  • Structural Biology
  • Image Processing

Background:

  • The contrast transfer function (CTF) is crucial for interpreting transmission electron microscope (TEM) images, but it often causes distortion.
  • Many TEM users, especially those new to the field, struggle with understanding and accurately estimating CTF parameters.
  • Existing software for CTF estimation produces results that are difficult to compare, hindering the selection of optimal parameters for image processing.

Purpose of the Study:

  • To develop a standardized graphical output for assessing CTF fit quality.
  • To introduce a new quantitative metric, CTF resolution, for evaluating CTF estimation robustness.
  • To provide tools for users to better assess CTF parameters and select the best estimation for their data.

Main Methods:

  • Presentation of a common graphical output to visualize CTF fit quality.
  • Introduction of CTF resolution, a novel measurement based on the correlation falloff of CTF oscillations.
  • Development of a quantitative metric for high-throughput screening of CTF estimations.

Main Results:

  • The proposed graphical output clearly demonstrates CTF fit quality, independent of specific estimation software.
  • CTF resolution provides a robust numerical metric for evaluating the quality of CTF estimations.
  • The new methods facilitate the selection of optimal CTF parameters for individual micrographs.

Conclusions:

  • The developed CTF visualizations and quantitative measures empower users to assess and select appropriate CTF parameters.
  • These tools enhance the reliability of image processing in transmission electron microscopy.
  • Improved CTF estimation leads to higher quality structural data from TEM.