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Related Concept Videos

Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

121
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....
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Frequency-Domain Interpretation of PD Control01:24

Frequency-Domain Interpretation of PD Control

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Proportional-Derivative (PD) controllers are widely used in fan control systems to improve stability and performance. A fan control system can be effectively represented using a Bode plot to illustrate the impact of a PD controller through its transfer function. The Bode plot visually conveys how PD control modifies the fan's response across various frequencies, providing a frequency domain interpretation of the controller's behavior.
The proportional control gain, combined with the...
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Time and frequency -Domain Interpretation of Phase-lag Control01:21

Time and frequency -Domain Interpretation of Phase-lag Control

135
Phase-lag controllers are widely used in control systems to improve stability and reduce steady-state errors. A dimmer switch controlling the brightness of a light bulb serves as a practical example of phase-lag control, gradually adjusting the bulb's brightness. Mathematically, phase-lag control or low-pass filtering is represented when the factor 'a' is less than 1.
Phase-lag controllers do not place a pole at zero, but instead influence the steady-state error by amplifying any...
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Frequency Response of Op Amp Circuits01:20

Frequency Response of Op Amp Circuits

382
Operational amplifiers (op-amp) are used in signal conditioning, filtering, or for performing mathematical operations such as addition, subtraction, integration, and differentiation. The frequency response of an op-amp is an important aspect that describes how the gain of the amplifier varies with frequency.
Frequency Response and Gain:
The gain of the op-amp, A(ω), is not a constant but a function of the input signal frequency. An op-amp can maintain a constant gain at low frequencies,...
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Time and frequency -Domain Interpretation of Phase-lead Control01:24

Time and frequency -Domain Interpretation of Phase-lead Control

122
Phase-lead controllers are commonly used in various control systems to enhance response speed and stability. Adjusting the brightness on a television screen offers a practical example of phase-lead control. When contrast is enhanced, a phase-lead controller is employed. Mathematically, phase-lead control is identified when the first parameter is smaller than the second.
The design of phase-lead control involves the strategic placement of poles and zeros to balance steady-state error and system...
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Scaling01:26

Scaling

290
In designing and analyzing filters, resonant circuits, or circuit analysis at large, working with standard element values like 1 ohm, 1 henry, or 1 farad can be convenient before scaling these values to more realistic figures. This approach is widely utilized by not employing realistic element values in numerous examples and problems; it simplifies mastering circuit analysis through convenient component values. The complexity of calculations is thereby reduced, with the understanding that...
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Updated: Aug 15, 2025

Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques
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Noise equalization scheme based on complex-valued ANN for multiple-eigenvalue modulated nonlinear frequency division

Xiuhua Lv, Chenglin Bai, Qi Qi

    Applied Optics
    |January 6, 2023
    PubMed
    Summary
    This summary is machine-generated.

    A novel noise equalization scheme using complex-valued artificial neural networks (c-ANN) significantly improves nonlinear frequency division multiplexing (NFDM) systems. This advanced method enhances performance by mitigating noise effects on received eigenvalues and discrete spectra, boosting data transmission accuracy.

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    Area of Science:

    • Optical communication systems
    • Signal processing
    • Artificial intelligence in telecommunications

    Background:

    • Noise in nonlinear frequency division multiplexing (NFDM) systems degrades the accuracy of nonlinear Fourier transform (NFT) algorithms.
    • This degradation is exacerbated by an increasing number of eigenvalues and higher-order modulation formats.
    • Perturbations in received eigenvalues and discrete spectra significantly impact system performance.

    Purpose of the Study:

    • To propose a novel noise equalization scheme for multiple-eigenvalue modulated NFDM systems.
    • To effectively mitigate the impact of noise on system performance.
    • To improve the accuracy of eigenvalue and discrete spectrum recovery.

    Main Methods:

    • Development of a noise equalization scheme utilizing a complex-valued artificial neural network (c-ANN).
    • Inputting eigenvalue perturbations and impaired discrete spectra into the c-ANN in complex form.
    • Constructing a complex-valued logic structure incorporating amplitude and phase information for feature reuse.

    Main Results:

    • The proposed c-ANN scheme significantly outperforms traditional NFT receiving without equalization, achieving 1 to 2 orders of magnitude improvement in bit error rate (BER).
    • In long-haul simulations with seven-eigenvalue modulation, a 64APSK signal achieved over 800 km transmission with BER meeting the 7% forward error correction (FEC) threshold, extending reach by 600 km.
    • Spectral efficiency reached 1.85 bit/s/Hz, and the scheme demonstrated superior equalization performance with reduced complexity compared to existing methods.

    Conclusions:

    • The proposed c-ANN based noise equalization scheme is highly effective for multiple-eigenvalue modulated NFDM systems.
    • The scheme successfully reduces noise impact, enabling reliable long-haul data transmission with high spectral efficiency.
    • This approach offers a promising solution for enhancing the robustness and performance of future optical communication networks.