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Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

85
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....
85
Upsampling01:22

Upsampling

195
Managing signal sampling rates is essential in digital signal processing to maintain signal integrity. A decimated signal, characterized by a reduced frequency range due to its lower sampling rate, can be upsampled by inserting zeros between each sample. This upsampling process expands the original spectrum and introduces repeated spectral replicas at intervals dictated by the new Nyquist frequency. To refine this zero-inserted sequence, it is passed through a lowpass filter with a cutoff...
195
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

60
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,...
60
Cascaded Op Amps01:16

Cascaded Op Amps

581
Operational amplifiers (op-amps) are versatile electronic components that can be interconnected in a cascade - one after another in a linear sequence. This cascading is possible due to their infinite input resistance and zero output resistance, allowing them to maintain their input-output relationships even when connected in series.
In a cascaded system, each op-amp is referred to as a stage. The output of one stage drives the input of the subsequent stage. As the input signal passes through...
581
Design Example: Capacitance Multiplier Circuit01:20

Design Example: Capacitance Multiplier Circuit

686
In integrated circuit technology, a capacitance multiplier is often utilized to produce a larger capacitance value when a small physical capacitance falls short. This is achieved by a circuit that multiplies capacitance values by a factor of up to 1000, such that a 10-pF capacitor can replicate the performance of a 100-nF capacitor.
The circuit illustrated in Figure 1 below incorporates two op-amps, with the first operating as a voltage follower and the second acting as an inverting amplifier.
686
Linear time-invariant Systems01:23

Linear time-invariant Systems

209
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...
209

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Related Experiment Video

Updated: May 30, 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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Low complexity neural network equalizer for nonlinearity mitigation in digital subcarrier multiplexing systems.

Sasipim Srivallapanondh, Pedro Freire, Giuseppe Parisi

    Optics Express
    |January 29, 2025
    PubMed
    Summary

    Neural network (NN) models, specifically biLSTM and 1D-CNN, significantly reduce computational complexity for nonlinearity compensation in digital subcarrier multiplexing (DSCM) optical systems. Weight clustering further enhances this reduction, offering a promising solution for optical nonlinear equalizers.

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    Area of Science:

    • Optical Communications
    • Machine Learning in Communications
    • Signal Processing

    Background:

    • Digital subcarrier multiplexing (DSCM) systems face performance degradation due to signal nonlinearities.
    • Traditional compensation methods like chromatic dispersion compensation (CDC) and digital back-propagation (DBP) have limitations in complexity and effectiveness.
    • Neural network (NN) models offer potential for advanced nonlinearity compensation.

    Purpose of the Study:

    • To comparatively study the complexity reduction of NN models for nonlinearity compensation in DSCM optical systems.
    • To evaluate the performance of NN-based equalizers against traditional methods and prior NN approaches.
    • To investigate the impact of weight clustering on NN computational complexity.

    Main Methods:

    • Implementation of NN models utilizing bi-directional long short-term memory (biLSTM) and 1D-convolutional NN (1D-CNN) layers.
    • Application of weight clustering technique to reduce the computational complexity of the NN models.
    • Comparative performance analysis using Q-factor and computational complexity metrics against CDC, DBP, and a perturbation analysis-based NN.

    Main Results:

    • The proposed NN-based equalizer achieves competitive Q-factor improvements.
    • Weight clustering significantly reduces NN computational complexity, by up to 91.1% compared to perturbation analysis NNs and 31.5% compared to DBP (1 step/span).
    • NN-based approaches demonstrate high-performance nonlinear compensation with substantially lower computational demands.

    Conclusions:

    • NN-based nonlinearity compensation, particularly with weight clustering, is highly effective in DSCM optical systems.
    • These optimized NN models offer a promising, computationally efficient alternative to traditional compensation techniques.
    • The study highlights the potential of NN approaches for future high-performance optical nonlinear equalizers.