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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
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

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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....
434
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 to State Space01:23

Transfer Function to State Space

953
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...
953
State Space to Transfer Function01:21

State Space to Transfer Function

682
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:
682
Electrical Systems01:21

Electrical Systems

923
In electrical engineering, the analysis of networks composed of passive linear components — resistors (R), capacitors (C), and inductors (L) — is fundamental. These components are organized into circuits where the relationship between input and output can be analyzed using transfer functions. The transfer function of an RLC circuit, which relates the voltage across a capacitor to the input voltage, can be derived using Kirchhoff's laws.
To derive the transfer function, consider an RLC...
923

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Updated: Apr 4, 2026

Characterization of Surface Modifications by White Light Interferometry: Applications in Ion Sputtering, Laser Ablation, and Tribology Experiments
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Filtering Non-Linear Transfer Functions on Surfaces.

Eric Heitz, Derek Nowrouzezahrai, Pierre Poulin

    IEEE Transactions on Visualization and Computer Graphics
    |September 11, 2015
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    Summary
    This summary is machine-generated.

    This study introduces a novel, efficient method for filtering non-linear transfer functions in computer graphics, significantly improving visual detail and reducing aliasing for realistic rendering.

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    Area of Science:

    • Computer Graphics
    • Rendering Algorithms
    • Image Processing

    Background:

    • Non-linear transfer functions enhance visual detail in rendering by mapping procedural functions, surface attributes, or geometry.
    • Efficient and accurate filtering of these functions is crucial for reducing aliasing across various viewing distances but remains an open problem due to complexity and perspective effects.

    Purpose of the Study:

    • To develop an accurate and efficient method for filtering non-linear transfer functions in computer graphics.
    • To address the challenges posed by complex, non-linear functions, procedural noise, geometry-dependent mappings, and perspective/masking effects.
    • To enable high-performance, real-time rendering with enhanced visual fidelity.

    Main Methods:

    • Computing and sampling specialized filtering distributions on the fly.
    • Utilizing Gaussian statistics for a novel representation of color map distributions over pixel footprints.
    • Developing view- and light-dependent filtering for micro-surface details, handling masking and occlusion.

    Main Results:

    • Achieved highly accurate filtering of transfer functions, matching ground truth.
    • Demonstrated very fast performance suitable for real-time applications.
    • Developed a framework compatible with color maps on textures, geometric details, and surface geometry warping.

    Conclusions:

    • The proposed filtering approach effectively solves the problem of accurately filtering complex non-linear transfer functions.
    • The method is computationally efficient, requires minimal shader code, and has a negligible memory footprint.
    • The framework is generalizable to other rendering quantities and applications, including shading with environment maps and geometry warping.