Search research articles

Related Concept Videos

Second Order systems II

Second Order systems II

In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.

Design Example: Underdamped Parallel RLC Circuit

Design Example: Underdamped Parallel RLC Circuit

Consider designing an oscillator circuit, a crucial component in various electronic devices and systems. The objective is to create an oscillator circuit with specific characteristics: a damped natural frequency of 4 kHz and a damping factor of 4 radians per second. To accomplish this, a parallel RLC circuit is employed, known for its ability to sustain oscillations at a resonant frequency. In this case, the damping factor is pivotal in achieving the desired performance.
Starting with a fixed...

Types of Damping

Types of Damping

If the amount of damping in a system is gradually increased, the period and frequency start to become affected because damping opposes, and hence slows, the back and forth motion (the net force is smaller in both directions). If there is a very large amount of damping, the system does not even oscillate; instead, it slowly moves toward equilibrium. In brief, an overdamped system moves slowly towards equilibrium, whereas an underdamped system moves quickly to equilibrium but will oscillate about...

Exponential and Sinusoidal Signals

Exponential and Sinusoidal Signals

The exponential function is crucial for characterizing waveforms that rise and decay rapidly. This continuous-time exponential function is defined using exponential terms with constants α and A. When both constants are real, the function is represented as,

Linear Approximation in Time Domain

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,...

RLC Circuit as a Damped Oscillator

RLC Circuit as a Damped Oscillator

An RLC circuit combines a resistor, inductor, and capacitor, connected in a series or parallel combination.
Consider a series RLC circuit. Here, the presence of resistance in the circuit leads to energy loss due to joule heating in the resistance. Therefore, the total electromagnetic energy in the circuit is no longer constant and decreases with time. Since the magnitude of charge, current, and potential difference continuously decreases, their oscillations are said to be damped. This is...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same journal

Quantitative evaluation of surface crack depth based on wideband surface waves electromagnetic acoustic transducer.

The Review of scientific instruments·2026

Same journal

A tetrahedral probe constellation approach for measuring canonical momentum in self-organized laboratory plasma.

The Review of scientific instruments·2026

Same journal

High-precision and short duration operating time dispersion in a fast mechanical switch driven by an ultrasonic motor: Modeling, prediction, and compensation.

The Review of scientific instruments·2026

Same journal

Cluster assisted soft-landing hub (CLASH): An instrument for surface desorption and deposition using a pulsed cluster ion source.

The Review of scientific instruments·2026

Same journal

Influence of pre-ionization parameters on multi-channel discharge characteristics of field-distortion switch gaps.

The Review of scientific instruments·2026

Same journal

A Joule-Thomson low-temperature scanning tunneling microscope with vector magnet and rotatable scanning head.

The Review of scientific instruments·2026

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Search research articles

Related Experiment Video

Updated: Oct 21, 2025

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

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

Parameter estimation for a damped real-valued sinusoid in noise.

Haitao Xu¹, Shengxi Zhou¹, Bo Yan²

¹Research and Development Institute in Shenzhen, Northwestern Polytechnical University, Shenzhen 518057, People's Republic of China.

The Review of Scientific Instruments

|September 2, 2021

Summary

This summary is machine-generated.

A new discrete Fourier transform (DFT) algorithm accurately estimates parameters of damped real-valued sinusoids. It effectively removes negative frequency interference for improved signal analysis.

More Related Videos

Experimental Methods to Study Human Postural Control

Experimental Methods to Study Human Postural Control

Published on: September 11, 2019

Simulation of Human-induced Vibrations Based on the Characterized In-field Pedestrian Behavior

Simulation of Human-induced Vibrations Based on the Characterized In-field Pedestrian Behavior

Published on: April 13, 2016

Related Experiment Videos

Last Updated: Oct 21, 2025

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

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

Experimental Methods to Study Human Postural Control

Experimental Methods to Study Human Postural Control

Published on: September 11, 2019

Simulation of Human-induced Vibrations Based on the Characterized In-field Pedestrian Behavior

Simulation of Human-induced Vibrations Based on the Characterized In-field Pedestrian Behavior

Published on: April 13, 2016

Area of Science:

Signal Processing
Spectral Analysis

Background:

Accurate parameter estimation of damped real-valued sinusoids is crucial in various scientific and engineering fields.
Existing discrete Fourier transform (DFT)-based methods often struggle with negative frequency interference, impacting parameter accuracy.

Purpose of the Study:

To introduce a novel three-point interpolation algorithm utilizing DFT for enhanced estimation of frequency and damping factor in damped real-valued sinusoids.
To comprehensively address and mitigate the contribution of negative frequency components to parameter estimation.

Main Methods:

The proposed algorithm employs specific DFT spectral bins (maximum amplitude and two arbitrary bins) within the rectangular window's main lobe.
It completely removes negative-frequency interference by strategically selecting these bins.
Performance is evaluated through simulations, analyzing the impact of sample length, zero-padding, and spectral bin selection on the mean-square error (MSE) to Crámer-Rao lower bound ratio.

Main Results:

Simulations demonstrate the algorithm's effectiveness in mitigating negative frequency interference.
The study analyzes the influence of sample length and zero-padding on algorithm performance.
Mean-square errors (MSEs) of estimated parameters are calculated and compared against state-of-the-art DFT-based algorithms.

Conclusions:

The presented three-point interpolation DFT algorithm provides accurate parameter estimation for damped real-valued sinusoids.
It offers a significant improvement over existing DFT-based methods by effectively handling negative frequency interference.
The algorithm's computational complexity is analyzed, confirming its practical viability.