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Related Concept Videos

State Space Representation01:27

State Space Representation

214
The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
214
State Space to Transfer Function01:21

State Space to Transfer Function

215
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:
215
Transfer Function to State Space01:23

Transfer Function to State Space

271
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...
271
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

85
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,...
85
Discrete-Time Fourier Series01:20

Discrete-Time Fourier Series

280
The Discrete-Time Fourier Series (DTFS) is a fundamental concept in signal processing, serving as the discrete-time counterpart to the continuous-time Fourier series. It allows for the representation and analysis of discrete-time periodic signals in terms of their frequency components. Unlike its continuous counterpart, which utilizes integrals, the calculation of DTFS expansion coefficients involves summations due to the discrete nature of the signal.
For a discrete-time periodic signal x[n]...
280
Interference: Path Lengths01:10

Interference: Path Lengths

1.3K
Consider two sources of sound, that may or may not be in phase, emitting waves at a single frequency, and consider the frequencies to be the same.
Two special sources may be considered when they are in phase. This can be easily achieved by feeding the two sources from the same source. An example would be synchronizing the two speakers by feeding them with the same source, such as the sound waves produced by a tuning fork. This setup ensures that the two sources have the same frequency and are...
1.3K

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Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
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State-space modeling approach for fringe pattern demodulation.

Shikha Sharma, Rishikesh Kulkarni

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    |October 19, 2023
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    Summary
    This summary is machine-generated.

    This study introduces a novel spatial carrier fringe demodulation technique using state-space modeling for precise phase estimation. The method enhances noise robustness and accuracy compared to existing approaches.

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    Area of Science:

    • Optics and Photonics
    • Signal Processing
    • Metrology

    Background:

    • Accurate phase estimation is crucial in optical metrology and interferometry.
    • Existing fringe demodulation techniques often struggle with noise and complex background variations.
    • State-space modeling offers a robust framework for dynamic system estimation.

    Purpose of the Study:

    • To propose a novel spatial carrier fringe demodulation technique for enhanced phase estimation.
    • To simultaneously estimate fringe background intensity, carrier frequency, and phase quadrature components.
    • To evaluate the proposed method's performance against established techniques.

    Main Methods:

    • A state-space modeling approach is employed for phase estimation.
    • The extended Kalman filter is utilized for state estimation.
    • Simultaneous estimation of fringe parameters is achieved within the state vector.

    Main Results:

    • The proposed technique demonstrates improved noise robustness.
    • Phase estimation accuracy is significantly enhanced compared to conventional methods.
    • Both simulation and experimental results validate the method's effectiveness.

    Conclusions:

    • The state-space modeling approach provides an effective solution for spatial carrier fringe demodulation.
    • The extended Kalman filter-based method offers superior performance in noisy environments.
    • This technique advances phase estimation accuracy in optical measurement applications.