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Related Concept Videos

Linear time-invariant Systems01:23

Linear time-invariant Systems

253
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...
253
BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

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System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....
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Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

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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,...
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Time and frequency -Domain Interpretation of Phase-lead Control01:24

Time and frequency -Domain Interpretation of Phase-lead Control

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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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Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

89
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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Properties of the z-Transform I01:17

Properties of the z-Transform I

190
The z-transform is a fundamental tool in digital signal processing, enabling the analysis of discrete-time systems through its various properties. It is an invaluable tool for analyzing discrete-time systems, offering a range of properties that simplify complex signal manipulations. One fundamental property is linearity. For any two discrete-time signals, the z-transform of their linear combination equals the same linear combination of their individual z-transforms. This property is essential...
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Optimizing FPGA implementation of high-precision chaotic systems for improved performance.

Issam Damaj1, Ashraf Zaher2, Wafic Lawand3

  • 1Department of Engineering, Cardiff School of Technologies, Cardiff Metropolitan University, Cardiff, United Kingdom.

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|April 9, 2024
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Summary

This study presents high-speed Field Programmable Gate Array (FPGA) cores for chaotic systems, achieving high throughput and precision for secure communication and data encryption applications.

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Area of Science:

  • Digital hardware implementation of chaotic systems.
  • Field-Programmable Gate Array (FPGA) core development.

Background:

  • Chaotic systems-on-a-chip offer significant potential for secure communication, data encryption, and random number generation.
  • Digital implementations of chaotic systems require high performance in speed, complexity, and precision.

Purpose of the Study:

  • To develop high-speed FPGA cores for chaotic systems, specifically the Lorenz system.
  • To implement numerical integration techniques for sixth-order chaotic equations with high precision.

Main Methods:

  • Developed FPGA cores using numerical integration techniques for chaotic systems.
  • Analyzed and evaluated cores based on algorithm complexity, precision, hardware area, throughput, power consumption, and operational frequency.
  • Validated designs through simulations and comparisons with existing literature.

Main Results:

  • Achieved highly efficient sixth-order Lorenz discretizations with 3.39 Gbps throughput and 16-bit precision.
  • Obtained 21.17 Gbps throughput with 64-bit precision for first-order implementation.
  • Demonstrated benchmark performance surpassing similar investigations.

Conclusions:

  • Successfully created high-performance FPGA cores for chaotic systems.
  • The developed cores offer superior throughput and precision, setting new benchmarks in the field.
  • These advancements are crucial for next-generation secure communication and data processing systems.