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Related Concept Videos

Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

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.
Linear time-invariant Systems01:23

Linear time-invariant Systems

A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be calculated...
Reconstruction of Signal using Interpolation01:10

Reconstruction of Signal using Interpolation

Signal processing techniques are essential for accurately converting continuous signals to digital formats and vice versa. When a continuous signal is sampled with a period T, the resulting sampled signal exhibits replicas of the original spectrum in the frequency domain, spaced at intervals equal to the sampling frequency. To handle this sampled signal, a zero-order hold method can be applied, which creates a piecewise constant signal by retaining each sample's value until the next sampling...
Real-World Applications of Space Curves01:29

Real-World Applications of Space Curves

Modern aerospace navigation depends on the accurate prediction of motion in three-dimensional space. In defense applications, radar systems continuously track both interceptors and moving aerial targets to find whether their flight paths will result in a collision. These motions are modeled mathematically as space curves, which represent paths that change continuously with time. Each object’s position is described by a vector function that specifies its location in terms of time-dependent...
Properties of DTFT I01:24

Properties of DTFT I

In signal processing, Discrete-Time Fourier Transforms (DTFTs) play a critical role in analyzing discrete-time signals in the frequency domain. Various properties of the DTFTs such as linearity, time-shifting, frequency-shifting, time reversal, conjugation, and time scaling help understand and manipulate these signals for different applications.
The linearity property of DTFTs is fundamental. If two discrete-time signals are multiplied by constants a and b respectively, and then combined to...

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Updated: Jun 28, 2026

Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques
09:01

Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques

Published on: April 4, 2017

Computationally efficient spline-based time delay estimation.

Francesco Viola, William F Walker

    IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control
    |November 7, 2008
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces computationally efficient algorithms for time delay estimation using cubic splines. The new methods maintain high accuracy, offering a superior alternative to existing algorithms for signal processing applications.

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    Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques
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    Using Neuron Spiking Activity to Trigger Closed-Loop Stimuli in Neurophysiological Experiments

    Published on: November 12, 2019

    Area of Science:

    • Signal Processing
    • Numerical Analysis

    Background:

    • Accurate time delay estimation is crucial in various fields, including communications and medical imaging.
    • Previous spline-based methods offered high accuracy but lacked computational efficiency.

    Discussion:

    • This paper presents optimized formulations of a spline-based time delay estimator.
    • The enhanced algorithms leverage cubic splines for continuous signal representation and analytical matching.
    • Computational efficiency is improved without compromising accuracy.

    Key Insights:

    • The proposed algorithms achieve bias and standard deviation comparable to the original spline-based method.
    • Performance is validated through computer simulations and ultrasound experiments.
    • These efficient formulations are superior to other published time delay estimation algorithms.

    Outlook:

    • Further research could explore applications in real-time systems.
    • Potential for integration into advanced sensor fusion techniques.
    • Adaptation for different signal types and noise conditions.