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Related Concept Videos

Passive Filters01:27

Passive Filters

563
Passive filters are utilized to shape the frequency spectrum of signals across a diverse array of applications. These filters, using only passive elements like resistors (R), inductors (L), and capacitors (C), are capable of selectively allowing or blocking certain frequency ranges without the need for external power sources.
Low-Pass Filters
Low-pass filters are designed to transmit signals with frequencies lower than the cutoff frequency, ωc, and attenuate those above it. The cutoff...
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Routh-Hurwitz Criterion I01:15

Routh-Hurwitz Criterion I

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Consider an electrical power grid, where stability is essential to prevent blackouts. The Routh-Hurwitz criterion is a valuable tool for assessing system stability under varying load conditions or faults. By analyzing the closed-loop transfer function, the Routh-Hurwitz criterion helps determine whether the system remains stable.
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...
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Routh-Hurwitz Criterion II01:19

Routh-Hurwitz Criterion II

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In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
304
Curvilinear Motion: Rectangular Components01:23

Curvilinear Motion: Rectangular Components

506
Curvilinear motion characterizes the movement of a particle or object along a curved path, notably evident when envisioning a car navigating a winding road. If the car starts at point A, its position vector is established within a fixed frame of reference, where the ratio of the position vector to its magnitude signifies the unit vector pointing in the position vector's direction.
As the car advances, its position evolves over time. Quantifying the car's velocity involves computing the...
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Active Filters01:25

Active Filters

865
Active filters are electronic circuits that use operational amplifiers (op-amps), resistors, and capacitors to filter out unwanted frequency components from a signal. A first-order low-pass active filter is designed to pass signals with a frequency lower than a certain cutoff frequency and attenuate frequencies higher than that cutoff frequency. The transfer function for a first-order low-pass active filter is:
865
Divergence and Stokes' Theorems01:06

Divergence and Stokes' Theorems

1.7K
The divergence and Stokes' theorems are a variation of Green's theorem in a higher dimension. They are also a generalization of the fundamental theorem of calculus. The divergence theorem and Stokes' theorem are in a way similar to each other; The divergence theorem relates to the dot product of a vector, while Stokes' theorem relates to the curl of a vector. Many applications in physics and engineering make use of the divergence and Stokes' theorems, enabling us to write...
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Updated: Jul 28, 2025

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
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Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

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Adaptive filter with Riemannian manifold constraint.

Jose Mejia1, Boris Mederos2, Nelly Gordillo1

  • 1Department of Electrical and Computer Engineering, Universidad Autónoma de Ciudad Juárez, 32310, Ciudad Juárez, Mexico.

Scientific Reports
|June 2, 2023
PubMed
Summary
This summary is machine-generated.

This study introduces a novel adaptive filter designed for non-linear manifold data, extending filtering to non-Euclidean spaces. The proposed manifold-based least-mean-squared algorithm demonstrates superior performance in various filtering tasks.

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Area of Science:

  • Signal Processing
  • Machine Learning
  • Geometric Data Analysis

Background:

  • Adaptive filtering algorithms typically assume Euclidean space, limiting their application to non-linear manifold data.
  • Processing data residing on manifolds requires specialized techniques beyond standard Euclidean methods.

Purpose of the Study:

  • To develop and evaluate an adaptive filter capable of operating directly on data from non-linear manifolds.
  • To generalize adaptive filtering to non-Euclidean spaces.

Main Methods:

  • Generalization of the least-mean-squared (LMS) algorithm to manifold spaces.
  • Utilizing the exponential map for operations within the manifold.

Main Results:

  • The proposed manifold-based adaptive filter effectively processes data in non-Euclidean spaces.
  • Experimental results show superior performance compared to existing state-of-the-art algorithms in several filtering tasks.

Conclusions:

  • The developed manifold adaptive filter provides a robust solution for signal processing on non-linear manifolds.
  • This work extends the applicability of adaptive filtering to a broader range of real-world scenarios involving complex data structures.