Pseudo-random Signal Generator Research Articles

Dynamics modeling of a memristor-based Rucklidge chaotic system: Multistability, offset boosting control and FPGA implementation

The complex dynamics greatly contributes to the application of chaos, especially the memristor chaotic systems that have emerged very recently. In this paper, a novel four-dimensional continuous chaotic system is developed by introducing a generalized memristor model into the classical Rucklidge system, and the rich dynamical traits are confirmed by theories and numerical simulations. System Hamilton energy is deduced and analyzed to expose the underlying energy evolution and chaos mechanism. And then, realizing the offset boosting control of the system promotes its engineering applications. Numerical simulations verify that the offset boosting controller can directly change the polarity of the chaotic signal. Specifically, bifurcation diagram, Lyapunov spectra, system complexity evolution diagram and dynamic evolution map are adopted to expound the rich dynamics. Meanwhile, the extreme multi-stability with various initial values resulting in an infinite number of coexisting attractors is also revealed. Finally, the proposed attractor is implemented using the Field Programmable Gate Array (FPGA) platform and building analog circuit based on Multisim. Among which, the former is potentially used to design the Pseudo-random signal generator in information encryption, while the latter is for verifying the existence of the proposed chaotic system.

Design of Pseudorandom Signal Generator Based on a Dual Memristor Chaotic System

This paper constructs a pseudo-random signal generator based on a dual memristor chaotic system. Firstly, the chaotic characteristics of the dual memristor chaotic system were explored through theoretical analysis and MATLAB numerical simulation, and a MULTISIM simulation circuit for the dual memristor chaotic system was constructed. Then, based on the threshold decision quantization method, a pseudorandom signal generator quantization circuit is formed by connecting an inverter amplifier and a hysteresis comparator on the output side of the analog circuit. Finally, the randomness of the pseudorandom sequence is discussed by NIST test and correlation analysis. The analysis results show that the pseudorandom sequence generated by the pseudo-random signal generator based on the dual memristor chaotic system exhibits good randomness.

TESTING OF PSEUDORANDOM SIGNAL GENERATORS BASED ON THE LORENTZ SYSTEM

This work presents results of the testing of modified pseudorandom signal generators. Two generators developed on the basis of the Lorentz system with chaotic dynamics are considered. The first generator is described by the Lorentz system implemented over a Galois field, and the second is described by the Lorentz system in which digital sequence formation occurs by periodic sampling from signal signatures. As an additional confirmation of the relevance of the results obtained, the article valuates a generator developed on the basis of the standard Matlab function for binary random sequence generating. Generator testing was carried out using a test battery developed by the National Institute of Standards and Technology, which includes 15 different tests. The results obtained are compared with the results obtained by testing reference generators. The results of this research can be applied in the development of cryptographic and data transmission systems.

A family of new generalized multi-scroll Hamiltonian conservative chaotic flows on invariant hypersurfaces and FPGA implementation

A family of new generalized multi-scroll Hamiltonian conservative chaotic systems(HCCSs) are firstly found by investigating Hamiltonian energy of a Hamiltonian conservative chaotic system. And the novelty of the family of new generalized multi-scroll HCCSs is that they are on some invariant hypersurfaces depending on Hamiltonian energy. Subsequently, some numerical analysis are given to show multi-scroll chaotic dynamics and complex characteristics of the family of new generalized multi-scroll HCCSs. Finally, FPGA circuits are employed to implement the family of new generalized multi-scroll HCCSs, which not only physically show the existence of multi-scroll dynamics, but also provide a family of new pseudo-random signal generators for engineering applications.

A Pseudo-Random Signal Generator for Offset Calibration Circuit

A pseudo-random signal generator based on 0.5μm CMOS technology is presented, and it is applied for an auto-zero operational amplifier. The generator circuit includes a linear feedback shift register for generating pseudo-random sequences, and a multi-level counter module for counting the system clock pulses. A group of pseudo-random codes generated by the linear feedback shift register are as the initial value of the counter. When the counter reaches the maximum value, the output of the counter will control the output signal to flip. At the same time, a new group of the pseudo-random code will reset the counter again, and finally generate a square wave signal whose frequency varies randomly. The generator circuit is simulated and verified. The simulation results show that the frequency of the output signal can vary from 2 kHz to 4 kHz with random characteristic. The generated pseudo-random signal can be used for the switching clock control of the auto-zero operational amplifier offset calibration circuit, so that the switching glitch of the auto-zero op-amp is random, which can significantly reduce the harmonics in the output signal of the op-amp.

A New Generalized Hamiltonian Chaotic System with Transient Quasi-Periodic Flows and Intermittent Chaos

The paper reports a new generalized Hamiltonian chaotic system with transient quasi-periodic flows and intermittent chaos by investigating the Kolmogorov-type transformation for a 3D chaotic system. The new system meets Hamiltonian energy conservation when [Formula: see text], and it is always conservative in volume because of a zero divergence. In addition, its Hamiltonian energy is found to be only related to the initial points. Subsequently, some dynamics analyses are presented to investigate its conservative characteristics and coexisting flows including periodic flows, quasi-periodic flows, and chaotic flows. Besides, both transient quasi-periodic flows and intermittent chaos are also found to occur, which further shows complex dynamics of the new generalized Hamiltonian chaotic system. Finally, an FPGA circuit is designed to implement the new generalized Hamiltonian chaotic system, and the results from the circuit experiments are consistent with those from numerical analyses. Complex dynamic characteristics existing in the new generalized Hamiltonian chaotic system seem more appropriate to be used in image encryption and secure communication. And the FPGA circuit not only shows the new generalized Hamiltonian chaotic system from a physical viewpoint, but also provides a new pseudo-random signal generator for engineering applications.

Design of a New 3D Chaotic System Producing Infinitely Many Coexisting Attractors and Its Application to Weak Signal Detection

This paper proposes a new 3D chaotic system, which can produce infinitely many coexisting attractors. By introducing a boosted control of cosine function to an original chaotic system, as the initial conditions periodically change, the proposed chaotic system can spontaneously output infinitely many chaotic sequences of different amplitudes in two directions in the phase plane. This means that the proposed system can output more key information as a pseudo-random signal generator (PRSG). This is of great significance in the research of weak signal detection. In comparison with the original chaotic system, the chaotic behavior of the proposed system is obviously enhanced due to the introduction of the boosted control function. Then, by adding the mathematical models of a weak signal and a noise signal to the proposed chaotic system, a new chaotic oscillator, which is sensitive to the weak signal, can be restructured. With the change of weak signal amplitude and angular frequency, the dynamical state of the detection system will generate a big difference, which indicates that the weak signal can be detected successfully. Finally, the proposed chaotic system model is physically realized by DSP (Digital Signal Processing), which shows its feasibility in industrial implementation. Especially, since a third-order chaotic system is the lowest-dimensional continuous system that can generate infinitely many coexisting attractors, the proposed chaotic system is of great value in the basic research of chaos.

Generating Infinitely Many Coexisting Attractors via a New 3D Cosine System and Its Application in Image Encryption

In this paper, a new third-order chaotic system which has extremely multistability is constructed by introducing the boosted control of cosine function. In comparison with other chaotic systems of extremely multistability, the proposed chaotic system can spontaneously generate the infinitely many coexisting attractors towards two directions of the phase plane. It indicates the proposed system can output more chaotic sequences of different amplitudes at the same time. This peculiar physical phenomena is very interesting and worth studying. Relative to original chaotic system, the chaos characteristic of the proposed system is obviously enhanced, the value of max Lyapunov exponent is increased significantly and the complexity value was higher. In particular, many periodic windows of the original chaotic system become chaos. It means the proposed chaotic system has better chaotic characteristics. If the new system is applied to the field of cryptography, it would be a better system model as a pseudo-random signal generator (PRSG). Then, the new image encryption algorithm is designed based on the proposed discrete system, and its safety performance is tested. The experimental results demonstrate the feasibility of its application in the field of cryptography.

Energy Conservation, Singular Orbits, and FPGA Implementation of Two New Hamiltonian Chaotic Systems

Since the conservative chaotic system (CCS) has no general attractors, conservative chaotic flows are more suitable for the chaos-based secure communication than the chaotic attractors. In this paper, two Hamiltonian conservative chaotic systems (HCCSs) are constructed based on the 4D Euler equations and a proposed construction method. These two new systems are investigated by equilibrium points, dynamical evolution map, Hamilton energy, and Casimir energy. They look similar, but it is found that one can be explained using Casimir power and another cannot be explained in terms of the mechanism of chaos. Furthermore, a pseudorandom signal generator is developed based on these proposed systems, which are tested based on NIST tests and implemented by using the field programmable gate array (FPGA) technique.

A new class of Hamiltonian conservative chaotic systems with multistability and design of pseudo-random number generator

• A new modeling method is employed to develop a class of high dimensional Hamiltonian conservative chaotic systems. • A new conservative hyperchaotic system is proposed and exhibits some behaviour previously unobserved. • Multistability including infinite-orbit and infinite-scroll is observed in the proposed systems. • For encryption, pseudo-random digital signal generators based on conservative chaotic systems are developed. Compared to dissipative chaotic system, conservative chaotic systems have some attractive features valuable for engineering applications, such as security communication. This paper proposes a method for constructing new high dimensional conservative chaotic systems, for instance 4 dimensional conservative chaotic systems and 5 dimensional conservative hyper-chaotic systems. The dynamic properties of the constructed systems are verified by the dynamical evolution map, equilibrium points, Lyapunov dimension, the volume of flow and the Hamiltonian energy. An interesting co-existence of quasi-period, chaos and hyper-chaos flows are observed in the developed conservative chaotic systems. With trigonometric transformation, parallel conservative chaotic systems are achieved with infinitely many scrolls. To accommodate the engineering application requirement, the security communication is considered as a case study. The proposed conservative chaotic systems passed the validation National Institute of Standard Statistic Test criteria for the pseudo-random property , which is the critical factor of security communication. Furthermore, the pseudo-random signal generator is developed using the Field Programmable Gate Array technique. Due to the complicated topology structure, such digital implementation was not commonly reported in literatures, instead most conservative chaotic systems were validated only by analog circuit simulation.

Study of Ranging System Using Pseudo-Random Continuous Wave Signal

Pseudo-random signal has potential value as ranging system’s signal since it has noise-like character, excellent autocorrelation and large time bandwidth character. The theory of the ranging system based on pseudo-random signal and how system works will be introduced in detail in this paper. We learned that the quality of signal generated by pseudo-random signal generator is very good through observing frequency domain chart, autocorrelation chart and time domain chart of signal. Quite accurate result can be got through dealing with experiment dates. It turned out that pseudo-random signal can be applied efficiently in ranging system and accuracy is quite high in field experiment. DOI : http://dx.doi.org/10.11591/telkomnika.v12i3.4458 Full Text: PDF

Design and Implementation of Digital Signal Transmission Performance Analyzer Based on FPGA

Digital signal transmission analyzer is mainly used for testing the transmission quality of digital communications signal and it usually composed of digital signal generator, pseudo-random signal generator, low-pass filter and digital signal analysis circuit. This study adopts FPGA to implement the digital signal generator and pseudo-random signal generator, as well as to implement the shift register to generate the required M sequence. By changing the low-pass filter cutoff frequency and the amplitude of the pseudo-random signal to analog transmission environment and signal analysis portion consists of the digital signal analysis circuit. The digital signal analysis module extracts the sync signal and produces synchronization scan signal by using the synchronous clock, as the outside trigger signal of oscilloscope to display the eye diagram of the digital signal stably. To analyze the degree of interference and the strength of inter-symbol interference by observing the eye diagram, thus this study implements the performance test for digital signal transmission.

Coding digital information with the use of generators with chaotic dynamics

A new method for coding graphic information is proposed. The method is based on the change in the color of each image symbol according to a pseudorandom law. Artificially designed self-oscillatory systems are used for generating a pseudorandom sequence of numbers. Results of studying the employed pseudorandom-signal generators and of encoding/decoding a color image are presented. The effect of damage in an encoded image on the restoration process is considered.

Application of pseudo-random signals and cross-correlation techniques in electroanalytical chemistry

The significance of application of white noise and cross-correlation function techniques in electroanalytical chemistry is described. The simplest pseudo-random signal generator and the correlator which avoid the use of large memory are constructed and applied to a few electrode systems. The responses obtained and their frequency profiles agree well with theoretical predictions.

Utilization of Recent Electronic Devices in Electrochemical Laboratory

The use of recent electronic devices such as linear IC (especially operational amplifiers), digital IC and various modules used to interface, are described for electrochemical applications. Those devices are treated as a ‘black box’, so that most chemists can use them as functional elements to construct various systems with no consideration of their inner principles. The present paper is divided into two parts ; the first half deals with analogue electronics and the second half with digital electronics. Analogue electronics is arranged in the following sections : 1) Analogue electronics as control elements. The basic principle of an operational amplifier is illustrated and then as an example of control use, a new electrolysis which is more general than usual chronopotentiometry or chronoamperometry is described, where the electrode potential and the current is controlled simultaneously. 2) Linear processing of analogue signals. Several simulation techniques are cited and criticized from a view point of laboratory use. CSDT (continuous space and discrete time) method and transfer function method are recommended as the simulation techniques for electrode processes. 3) Non-linear processing of analogue signals. An irreversible electode process including non-linear elements as exponential terms is cited and its simulator is given. 4) Analog switch. The principle of analogue switch is illustrated and application of it such as switching correlator and signal modulator are described. In last section of analogue electronics, promising devices such as phase-locked loop amplifier and photo-coupler as an isolator are described briefly. In digital electronics part, the importance of the knowledge for hardware is emphasized and several reasons for digitalization in measurements are interpreted. Then, the fundamentals of digital electronics are outlined briefly, assuming no previous knowledge of electronics. The operation of RS-flip-flow is given onsiderable space for understanding of the higher devices such as counters and shiftregisters. After fundamentals, digital electronics for polarographic applications are described as follows : 1) Long-period integrator for coulombmeter. The combination of V-f converter and counter is recommended as a digital coulombmeter in electrochemistry. 2) Signal generator. The use of digital IC as a signal generator is illustrated. Astable mutivibrator and monostable multivibrator are illustrated. Double-pulse generator is cited as the typical example of electrochemical use. Maximum-period signal generator is introduced as a pseudorandom signal generator. 3) Digital memory. Digital memory device for transient recording is illustrated. The device was constructed from ADC (10bit resolution and successive approximation type), DAC (10bit), MOS dynamic shift registers (10×1024 bit) and some gates for read/write control. The device was applied to electrochemical system to facilitate the correlation techniques. Typical results are illustrated. Possible use of the device is discussed. 4) Microcomputer. The use of one-chip c.p.u. for microcomputer organization isdiscussed. The possible construction of microprocesser in laboratory is described.

Application of pseudo-random signals and cross-correlation techniques in electroanalytical chemistry

Summary The significance of application of white noise and cross-correlation function techniques in electroanalytical chemistry is described. The simplest pseudo-random signal generator and the correlator which avoid the use of large memory are constructed and applied to a few electrode systems. The responses obtained and their frequency profiles agree well with theoretical predictions.