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Showing papers in "Circuits Systems and Signal Processing in 2016"


Journal ArticleDOI
TL;DR: The proposed algorithm has lower computational cost than the existing over-parameterization model-based RLS algorithm and the simulation results indicate that the proposed algorithm can effectively estimate the parameters of the nonlinear systems.
Abstract: In this paper, we study the parameter estimation problem of a class of output nonlinear systems and propose a recursive least squares (RLS) algorithm for estimating the parameters of the nonlinear systems based on the model decomposition. The proposed algorithm has lower computational cost than the existing over-parameterization model-based RLS algorithm. The simulation results indicate that the proposed algorithm can effectively estimate the parameters of the nonlinear systems.

121 citations


Journal ArticleDOI
TL;DR: In this paper, an improved Lyapunov-Krasovskii (L---K) functional is introduced to ensure robust synchronization of chaotic Lur'e systems with time-varying delays via sampled data control.
Abstract: This paper deals with the problem of robust $$H_{\infty }$$H? synchronization of chaotic Lur'e systems with time-varying delays via sampled-data control. In order to make full use of the information about sampling intervals, nonlinear functions and time-varying delays, an improved Lyapunov---Krasovskii (L---K) functional is introduced. Based on reciprocal convex combination technique, sufficient conditions are derived in terms of linear matrix inequalities (LMIs) to ensure the asymptotic synchronization of the considered Lur'e system with a guaranteed $$H_{\infty }$$H? performance. By solving the obtained LMIs, the required sampled-data control gain matrix is obtained, which assures the asymptotic stability of the error system and reduces the effect of external disturbance according to $$H_{\infty }$$H? norm. Finally, the effectiveness and less conservatism of the proposed method are verified through numerical simulations of the Chua's circuit and neural networks.

96 citations


Journal ArticleDOI
TL;DR: A three-dimensional autonomous chaotic system with a circular equilibrium with good qualitative agreement between the experimental results, PSpice and numerical simulations is investigated and chaos exists in this system with order less than three.
Abstract: A three-dimensional autonomous chaotic system with a circular equilibrium is investigated in this paper. Some dynamical properties and behaviors of this system are described in terms of equilibria, eigenvalue structures, bifurcation diagrams, Lyapunov exponents, time series and phase portraits. For specific parameters, the system displays periodic and chaotic attractors. The physical existence of the chaotic behavior found in the proposed system is verified by using the Orcad-PSpice software and experimental verification. A good qualitative agreement is shown between the experimental results, PSpice and numerical simulations. Furthermore, the commensurate fractional-order version of the system with a circular equilibrium is numerically studied. It is found that chaos exists in this system with order less than three. By tuning the commensurate fractional order, the system with a circular equilibrium displays chaotic and periodic attractors, respectively. Finally, chaos synchronization of identical fractional-order chaotic systems with a circular equilibrium is achieved by using the unidirectional linear error feedback coupling. It is shown that the fractional-order chaotic system can achieve synchronization for appropriate coupling strength.

79 citations


Journal ArticleDOI
TL;DR: A multi-objective optimization technique is used for controlling some filter specifications, which are the transition bandwidth, the stop band frequency gain and the maximum allowable peak in the filter pass band.
Abstract: This paper presents three different optimization cases for normalized fractional order low-pass filters (LPFs) with numerical, circuit and experimental results. A multi-objective optimization technique is used for controlling some filter specifications, which are the transition bandwidth, the stop band frequency gain and the maximum allowable peak in the filter pass band. The extra degree of freedom provided by the fractional order parameter allows the full manipulation of the filter specifications to obtain the desired response required by any application. The proposed mathematical model is further applied to a case study of a practical second- generation current conveyor (CCII)-based fractional low-pass filter. Circuit simulations are performed for two different fractional order filters, with orders 1.6 and 3.6, with cutoff frequencies 200 and 500 Hz, respectively. Experimental results are also presented for LPF of 4.46 kHz cutoff frequency using a fabricated fractional capacitor of order 0.8, proving the validity of the proposed design approach.

78 citations


Journal ArticleDOI
TL;DR: Optimal pole-zero approximation method in discrete form is proposed for realization of digital fractional order controller and shows better speed control of separately excited DC motor with the realized digital FO-PID controller than that of the integer order PID controller.
Abstract: The aim of paper is to employ digital fractional order proportional integral derivative (FO-PID) controller for speed control of buck converter fed DC motor. Optimal pole-zero approximation method in discrete form is proposed for realization of digital fractional order controller. The stand-alone controller is implemented on embedded platform using digital signal processor TMS320F28027. The five tuning parameters of controller enhance the performance of control scheme. For tuning of the controller parameters, dynamic particle swarm optimization technique is employed. The proposed control scheme is simulated on MATLAB and verified by experimental results. Performance comparison shows better speed control of separately excited DC motor with the realized digital FO-PID controller than that of the integer order PID controller.

69 citations


Journal ArticleDOI
TL;DR: This analysis examines the differences in least squares error, stability, $$-$$-3 dB frequency, higher-order implementations, and parameter sensitivity to determine the most suitable fractional-order order transfer function for the approximated Butterworth magnitude responses.
Abstract: Three fractional-order transfer functions are analyzed for differences in realizing ($$1+\alpha $$1+?) order lowpass filters approximating a traditional Butterworth magnitude response. These transfer functions are realized by replacing traditional capacitors with fractional-order capacitors ($$Z=1/s^{\alpha }C$$Z=1/s?C where $$0\le \alpha \le 1$$0≤?≤1) in biquadratic filter topologies. This analysis examines the differences in least squares error, stability, $$-$$-3 dB frequency, higher-order implementations, and parameter sensitivity to determine the most suitable ($$1+\alpha $$1+?) order transfer function for the approximated Butterworth magnitude responses. Each fractional-order transfer function for $$(1+\alpha )=1.5$$(1+?)=1.5 is realized using a Tow---Thomas biquad a verified using SPICE simulations.

68 citations


Journal ArticleDOI
TL;DR: A least-squares fitting routine is used to approximate the stopband ripple characteristics of fractional-order inverse Chebyshev lowpass filters which have fractional -order zeros and poles.
Abstract: In this paper we use a least-squares fitting routine to approximate the stopband ripple characteristics of fractional-order inverse Chebyshev lowpass filters which have fractional-order zeros and poles. MATLAB simulations of $$(1+\alpha )$$(1+�)-order lowpass filters with fractional steps from $$\alpha =0.1$$�=0.1 to $$\alpha =0.9$$�=0.9 are given as examples. SPICE simulations of 1.2-, 1.5-, and 1.8-order lowpass filters and experimental results of a 1.5-order filter using approximated fractional-order capacitors in a Multiple-Input Biquad circuit validate the implementation of these circuits.

61 citations


Journal ArticleDOI
TL;DR: This paper presents how a fractor can be realized, using RC ladder circuit, meeting the predefined specifications on both F and α, thus realizing dynamic fractors.
Abstract: A fractor is a simple fractional-order system. Its transfer function is $$1/Fs^{\alpha }$$1/Fs?; the coefficient, F, is called the fractance, and $$\alpha $$? is called the exponent of the fractor. This paper presents how a fractor can be realized, using RC ladder circuit, meeting the predefined specifications on both F and $$\alpha $$?. Besides, commonly reported fractors have $$\alpha $$? between 0 and 1. So, their constant phase angles (CPA) are always restricted between $$0^{\circ }$$0? and $$-90^{\circ }$$-90?. This work has employed GIC topology to realize fractors from any of the four quadrants, which means fractors with $$\alpha $$? between $$-$$-2 and +2. Hence, one can achieve any desired CPA between $$+180^{\circ }$$+180? and $$-180^{\circ }$$-180?. The paper also exhibits how these GIC parameters can be used to tune the fractance of emulated fractors in real time, thus realizing dynamic fractors. In this work, a number of fractors are developed as per proposed technique, their impedance characteristics are studied, and fractance values are tuned experimentally.

60 citations


Journal ArticleDOI
TL;DR: The proposed method first uses PCA to decrease the dimensions of the ECG signal training set and then employs KICA to calculate the feature space for extracting the nonlinear features, resulting in better classification results on the MIT–BIH arrhythmia database.
Abstract: Electrocardiogram (ECG) signal feature extraction is important in diagnosing cardiovascular diseases. This paper presents a new method for nonlinear feature extraction of ECG signals by combining principal component analysis (PCA) and kernel independent component analysis (KICA). The proposed method first uses PCA to decrease the dimensions of the ECG signal training set and then employs KICA to calculate the feature space for extracting the nonlinear features. Support vector machine (SVM) is utilized to determine the nonlinear features of the ECG signal classification. Genetic algorithm is also used to optimize the SVM parameters. The proposed method is advantageous because it does not require a huge amount of sampling data, and this technique is better than traditional strategies to select optimal features in the multi-domain feature space. Computer simulations reveal that the proposed method yields more satisfactory classification results on the MIT---BIH arrhythmia database, reaching an overall accuracy of 97.78 %.

58 citations


Journal ArticleDOI
TL;DR: Joint optimization of CSS, channel access and resource allocation is investigated in an overlay CRN in which each SU carries multi-channel spectrum sensing and transmits the detected energy to a fusion centre in the imperfect reporting channel.
Abstract: Cooperative spectrum sensing (CSS) that utilizes multi-user diversity to mitigate channel instability and noise uncertainty is a promising technique in cognitive radio networks (CRNs). However, the spectrum-sensing parameters which affect the channel-access opportunities of secondary users (SUs) are conventionally regarded as static and treated independently from the resource-allocation strategies. In this paper, joint optimization of CSS, channel access and resource allocation is investigated in an overlay CRN in which each SU carries multi-channel spectrum sensing and transmits the detected energy to a fusion centre in the imperfect reporting channel. An access factor is introduced to describe the channel-access strategies in both cooperative and non-cooperative schemes. Based on the aggregate interference and the transmit power constraints, an optimization problem of multi-channel CSS is formulated to obtain the optimal transmit powers, allocation-access strategies, and sensing threshold of CR system for maximization of the opportunistic throughput. To solve the non-convex problems in both the single and multiple CR systems, the efficient iterative algorithms are developed by exploiting the hidden convexity of the optimization problems. Numerical results show that the performance of our approaches yields a significant enhancement compared with the equal channel-access and equal power-allocation strategy.

57 citations


Journal ArticleDOI
TL;DR: Experimental results, with 100 % classification accuracy, on a real-world EEG signals database analysis illustrate the effectiveness of the proposed method for EEG signal classification.
Abstract: In this paper, we propose a method for the analysis and classification of electroencephalogram (EEG) signals using EEG rhythms. The EEG rhythms capture the nonlinear complex dynamic behavior of the brain system and the nonstationary nature of the EEG signals. This method analyzes common frequency components in multichannel EEG recordings, using the filter bank signal processing. The mean frequency (MF) and RMS bandwidth of the signal are estimated by applying Fourier-transform-based filter bank processing on the EEG rhythms, which we refer intrinsic band functions, inherently present in the EEG signals. The MF and RMS bandwidth estimates, for the different classes (e.g., ictal and seizure-free, open eyes and closed eyes, inter-ictal and ictal, healthy volunteers and epileptic patients, inter-ictal epileptogenic and opposite to epileptogenic zone) of EEG recordings, are statistically different and hence used to distinguish and classify the two classes of signals using a least-squares support vector machine classifier. Experimental results, with 100 % classification accuracy, on a real-world EEG signals database analysis illustrate the effectiveness of the proposed method for EEG signal classification.

Journal ArticleDOI
TL;DR: Simulation results have demonstrated that the proposed algorithm not only has better tracking capability than the existing subband adaptive filter algorithms, but also exhibits lower steady-state error.
Abstract: Proposed is a novel variable step size normalized subband adaptive filter algorithm, which assigns an individual step size for each subband by minimizing the mean square of the noise-free a posterior subband error. Furthermore, a noniterative shrinkage method is used to recover the noise-free priori subband error from the noisy subband error signal. Simulation results using the colored input signals have demonstrated that the proposed algorithm not only has better tracking capability than the existing subband adaptive filter algorithms, but also exhibits lower steady-state error.

Journal ArticleDOI
TL;DR: An optimal design of two-dimensional finite impulse response (2D FIR) filter with quadrantally even symmetric impulse response with fractional derivative constraints (FDCs) using HPSO-GSA is presented.
Abstract: In this article, an optimal design of two-dimensional finite impulse response (2D FIR) filter with quadrantally even symmetric impulse response using fractional derivative constraints (FDCs) is presented. Firstly, design problem of 2D FIR filter is formulated as an optimization problem. Then, FDCs are imposed over the integral absolute error for designing of the quadrantally even symmetric impulse response filter. The optimized FDCs are applied over the prescribed frequency points. Next, the optimized filter impulse response coefficients are computed using a hybrid optimization technique, called hybrid particle swarm optimization and gravitational search algorithm (HPSO-GSA). Further, FDC values are also optimized such that flat passband and stopband frequency response is achieved and the absolute $$L_1$$L1-error is minimized. Finally, four design examples of 2D low-pass, high-pass, band-pass and band-stop filters are demonstrated to justify the design accuracy in terms of passband error, stopband error, maximum passband ripple, minimum stopband attenuation and execution time. Simulation results have been compared with the other optimization algorithms, such as real-coded genetic algorithm, particle swarm optimization and gravitational search algorithm. It is observed that HPSO-GSA gives improved results for 2D FIR-FDC filter design problem. In comparison with other existing techniques of 2D FIR filter design, the proposed method shows improved design accuracy and flexibility with varying values of FDCs.

Journal ArticleDOI
TL;DR: A novel method for the nonlinear feature extraction of ECG signals by combining wavelet packet decomposition (WPD) and approximate entropy (ApEn) that does not require dimensionality reduction, has fast calculation speed, and requires simple computations is proposed.
Abstract: Electrocardiogram (ECG) signal classification is an important diagnosis tool wherein feature extraction plays a crucial function. This paper proposes a novel method for the nonlinear feature extraction of ECG signals by combining wavelet packet decomposition (WPD) and approximate entropy (ApEn). The proposed method first uses WPD to decompose ECG signals into different frequency bands and then calculates the ApEn of each wavelet packet coefficient as a feature vector. A support vector machine (SVM) classifier is used for the classification. The particle swarm optimization algorithm is used to optimize the SVM parameters. The proposed method does not require dimensionality reduction, has fast calculation speed, and requires simple computations. The classification of the signals into five beats yields an acceptable accuracy of 97.78 %.

Journal ArticleDOI
TL;DR: The simulation results demonstrate that the proposed sparse AP algorithm outperforms the conventional AP and previously reported sparse-aware AP algorithms in terms of both convergence speed and steady-state error when the system is sparse.
Abstract: In this paper, an improved sparse-aware affine projection (AP) algorithm for sparse system identification is proposed and investigated. The proposed sparse AP algorithm is realized by integrating a non-uniform norm constraint into the cost function of the conventional AP algorithm, which can provide a zero attracting on the filter coefficients according to the value of each filter coefficient. Low complexity is obtained by using a linear function instead of the reweighting term in the modified AP algorithm to further improve the performance of the proposed sparse AP algorithm. The simulation results demonstrate that the proposed sparse AP algorithm outperforms the conventional AP and previously reported sparse-aware AP algorithms in terms of both convergence speed and steady-state error when the system is sparse.

Journal ArticleDOI
TL;DR: Using the linear copositive Lyapunov function integrated with average dwell time switching technique, the finite-time stability of fractional order positive switched systems is addressed and a control strategy based on linear programming is designed.
Abstract: This paper is concerned with finite-time stability analysis and control synthesis of fractional order positive switched systems. By using the linear copositive Lyapunov function integrated with average dwell time switching technique, the finite-time stability of fractional order positive switched systems is first addressed. Then, the finite-time boundedness of fractional order positive switched systems with exogenous input is discussed. Finally, the stabilization of the considered systems is proposed, where a control strategy based on linear programming is designed. Several implemental algorithms are provided to reduce the conservativeness of results. Two numerical examples are given to show the effectiveness of the findings of theory.

Journal ArticleDOI
TL;DR: The aim of this paper is to present two efficient methods for digital realization of non-integer order filters: discrete time-domain Oustaloup approximation and Laguerre impulse response approximation.
Abstract: Typical approach to non-integer order filtering consists of analogue design and implementation. Digital realization of non-integer order systems is susceptible to problems such as infinite memory requirement and sensitivity to numerical errors. The aim of this paper is to present two efficient methods for digital realization of non-integer order filters: discrete time-domain Oustaloup approximation and Laguerre impulse response approximation. Properties of both methods are investigated with use of non-integer low-pass filter. Filters realized with presented methods are then used for filtering of EEG signal. Paper concludes with discussion of merits and flaws of both methods.

Journal ArticleDOI
TL;DR: The design examples demonstrate that reasonably smooth wavelets can be designed from the proposed filter banks and the performance of optimal filter banks has been found better in terms of joint time–frequency localization.
Abstract: We present a method for designing optimal biorthogonal wavelet filter banks (FBs). Joint time---frequency localization of the filters has been chosen as the optimality criterion. The design of filter banks has been cast as a constrained optimization problem. We design the filter either with the objective of minimizing its frequency spread (variance) subject to the constraint of prescribed time spread or with the objective of minimizing the time spread subject to the fixed frequency spread. The optimization problems considered are inherently non-convex quadratic constrained optimization problems. The non-convex optimization problems have been transformed into convex semidefinite programs (SDPs) employing the semidefinite relaxation technique. The regularity constraints have also been incorporated along with perfect reconstruction constraints in the optimization problem. In certain cases, the relaxed SDPs are found to be tight. The zero duality gap leads to the global optimal solutions. The design examples demonstrate that reasonably smooth wavelets can be designed from the proposed filter banks. The optimal filter banks have been compared with popular filter banks such as Cohen---Daubechies---Feauveau biorthogonal wavelet FBs, time---frequency optimized half-band pair FBs and maximally flat half-band pair FBs. The performance of optimal filter banks has been found better in terms of joint time---frequency localization.

Journal ArticleDOI
TL;DR: A qualified performance of the proposed SRAM cell is demonstrated in terms of power dissipation, power–delay product, write margin, read access time and sensitivity to process, voltage and temperature variations as compared to the other most efficient low-voltage SRAM cells previously presented in the literature.
Abstract: This paper presents a new nine-transistor (9T) SRAM cell operating in the subthreshold region. In the proposed 9T SRAM cell, a suitable read operation is provided by suppressing the drain-induced barrier lowering effect and controlling the body---source voltage dynamically. Proper usage of low-threshold voltage (L-$$V_{\mathrm{t}}$$Vt) transistors in the proposed design helps to reduce the read access time and enhance the reliability in the subthreshold region. In the proposed cell, a common bit-line is used in the read and write operations. This design leads to a larger write margin without using extra circuits. The simulation results at 90 nm CMOS technology demonstrate a qualified performance of the proposed SRAM cell in terms of power dissipation, power---delay product, write margin, read access time and sensitivity to process, voltage and temperature variations as compared to the other most efficient low-voltage SRAM cells previously presented in the literature.

Journal ArticleDOI
TL;DR: Switched-capacitor fractional-step filter design of low-pass filter prototypes with Butterworth characteristics is reported for the first time using discrete-time integrators which implement both the bilinear and the Al-Alaoui s-to-z transformations.
Abstract: Switched-capacitor fractional-step filter design of low-pass filter prototypes with Butterworth characteristics is reported in this work for the first time. This is achieved using discrete-time integrators which implement both the bilinear and the Al-Alaoui s-to-z transformations. Filters of orders 1.2, 1.5 and 1.8 as well as 3.2, 3.5, and 3.8 are designed and verified using transistor-level simulations with Cadence on AMS $$0.35\,\upmu $$0.35μm CMOS process. Digital programmability of the fractional-step filters is also achieved.

Journal ArticleDOI
TL;DR: A signal modulating circuit is used to verify the effectiveness of the enhanced inference operator on the D matrix, the R matrix and the DR matrix, which demonstrates the high efficiency of theEnhanced inference operator and the feasibility of the new hybrid diagnostic method.
Abstract: This paper is devoted to the fault diagnosis of electronic systems by combining logical signals, such as built-in test output, and analog signals, such as voltage, current and temperature. First, the basic inference principles of dependency matrix (D matrix) diagnosis and fuzzy diagnosis are introduced, and the characteristics of their inference operators are summarized. Then, the similarities and differences between the two diagnostic methods are analyzed. Based on the judgement of close degree, a new enhanced inference operator is defined to suit both the D matrix and the fuzzy relation matrix (R matrix). A DR matrix is defined to describe the mixed relationships between faults and the two types of signals. Based on the enhanced inference operator and the DR matrix, a new hybrid diagnostic method is established. Finally, a signal modulating circuit is used to verify the effectiveness of the enhanced inference operator on the D matrix, the R matrix and the DR matrix, which demonstrates the high efficiency of the enhanced inference operator and the feasibility of the new hybrid diagnostic method.

Journal ArticleDOI
TL;DR: In this paper, the authors examined certain classes of multiconnected (complex) systems with time-varying delay and derived delay-independent stability conditions and estimates of the convergence rate of solutions to the origin for those systems.
Abstract: This paper examines certain classes of multiconnected (complex) systems with time-varying delay. Delay-independent stability conditions and estimates of the convergence rate of solutions to the origin for those systems are derived. It is shown that the exponents in the obtained estimates depend on the parameters of Lyapunov functions constructed for the corresponding isolated subsystems. The problem of computing parameter values that provide the most precise estimates is investigated. Some examples are presented to demonstrate the effectiveness of the proposed approaches.

Journal ArticleDOI
TL;DR: The design, analysis, computer simulation, and experimental measurement of fractional-order sinusoidal oscillator with two current conveyors, two resistors, and two fractional immittance elements confirm the attractive features of the proposed oscillator.
Abstract: This paper deals with the design, analysis, computer simulation, and experimental measurement of fractional-order sinusoidal oscillator with two current conveyors, two resistors, and two fractional immittance elements. The used conveyor is based on the bulk-driven quasi-floating-gate technique in order to offer high threshold-to-supply voltage ratio and maximum input-to-supply voltage ratio. The supply voltage of the oscillator is 1 V, and the power consumption is $$74\,\upmu \hbox {W}$$74μW, and hence the proposed oscillator can be suitable for biomedical, portable, battery-powered, and other applications where the low-power consumption is critical. A number of equations along with graphs describing the theoretical properties of the oscillator are presented. The unique features of fractional-order oscillator are highlighted considering practical utilization, element computation, tuning, phase shift of output signals, sensitivities, etc. The simulations performed in the Cadence environment and the measurements of a real chip confirm the attractive features of the proposed oscillator.

Journal ArticleDOI
TL;DR: A simple and efficient image compression scheme, consisting of reversible color space transformation, quantization, subsampling, differential pulse code modulation and Golomb–Rice encoding, which achieves almost as high compression rate as can be achieved with existing DCT-based image compression methods, but with an order of reduced area and power consumption.
Abstract: An image compressor inside wireless capsule endoscope should have low power consumption, small silicon area, high compression rate and high reconstructed image quality. Simple and efficient image compression scheme, consisting of reversible color space transformation, quantization, subsampling, differential pulse code modulation (DPCM) and Golomb---Rice encoding, is presented in this paper. To optimize these methods and combine them optimally, the unique properties of human gastrointestinal tract image are exploited. Computationally simple and suitable color spaces for efficient compression of gastrointestinal tract images are proposed. Quantization and subsampling methods are optimally combined. A hardware-efficient, locally adaptive, Golomb---Rice entropy encoder is employed. The proposed image compression scheme gives an average compression rate of 90.35 % and peak signal-to-noise ratio of 40.66 dB. ASIC has been fabricated on UMC130nm CMOS process using Faraday high-speed standard cell library. The core of the chip occupies 0.018 mm$$^2$$2 and consumes 35 $$\upmu {\text {W}}$$μW power. The experiment was performed at 2 frames per second on a $$256\times 256$$256?256 color image. The power consumption is further reduced from 35 to 9.66 $$\upmu $$μW by implementing the proposed image compression scheme using Faraday low-leakage standard cell library on UMC130nm process. As compared to the existing DPCM-based implementations, our realization achieves a significantly higher compression rate for similar area and power consumption. We achieve almost as high compression rate as can be achieved with existing DCT-based image compression methods, but with an order of reduced area and power consumption.

Journal ArticleDOI
TL;DR: In this paper, a general analysis of the generation for all possible fractional order oscillators based on two-port network is presented and the general analytical formulas of the oscillation frequency and condition as well as the phase difference between the two oscillatory outputs are derived.
Abstract: In this paper, a general analysis of the generation for all possible fractional order oscillators based on two-port network is presented. Three different two-port network classifications are used with three external single impedances, where two are fractional order capacitors and a resistor. Three possible impedance combinations for each classification are investigated, which give nine possible oscillators. The characteristic equation, oscillation frequency and condition for each presented topology are derived in terms of the transmission matrix elements and the fractional order parameters $$\alpha $$ź and $$\beta $$β. Mapping between some cases is also illustrated based on similarity in the characteristic equation. The use of fractional order elements $$\alpha $$ź and $$\beta $$β adds extra degrees of freedom, which increases the design flexibility and frequency band, and provides extra constraints on the phase difference. Study of four different active elements, such as voltage-controlled current source, gyrator, op-amp-based network, and second-generation current-conveyor-based network, serve as a two-port network is presented. The general analytical formulas of the oscillation frequency and condition as well as the phase difference between the two oscillatory outputs are derived and summarized in tables for each designed oscillator network. A comparison between fractional order oscillators with their integer order counterparts is also illustrated where some designs cannot work in the integer case. Numerical Spice simulations and experimental results are given to validate the presented analysis.

Journal ArticleDOI
TL;DR: Interestingly, empirical results show that time–frequency optimal, filter banks of length nine, designed with the proposed methodology, have unit Sobolev regularity, which is maximum achievable with single vanishing moment.
Abstract: In this paper, we design three-band time---frequency-localized orthogonal wavelet filter banks having single vanishing moment. We propose new expressions to compute mean and variances in time and frequency from the samples of the Fourier transform of the asymmetric band-pass compactly supported wavelet functions. We determine discrete-time filter of length eight that generates the time---frequency optimal time-limited scaling and wavelet functions using cascade algorithm. Time---frequency product (TFP) of a function is defined as the product of its time variance and frequency variance. The TFP of the designed functions is close to 0.25 with unit Sobolev regularity. Three-band filter banks are designed by minimizing a weighted combination of TFPs of wavelets and scaling functions. Interestingly, empirical results show that time---frequency optimal, filter banks of length nine, designed with the proposed methodology, have unit Sobolev regularity, which is maximum achievable with single vanishing moment. Design examples for length six and length nine filter banks are given to demonstrate the effectiveness of the proposed design methodology.

Journal ArticleDOI
TL;DR: Results of analysis of transient states in a series circuit of the class RLβCα, supplied by an ideal voltage source, and effective relations enabling the determination of transient waveforms in a closed form are given.
Abstract: Results of analysis of transient states in a series circuit of the class $${RL}_{\beta }{C}_{\alpha }$$RLβC�, supplied by an ideal voltage source, have been described in the paper. This circuit consists of a coil $${L}_{\beta }$$Lβ and a supercapacitor $${C}_{\alpha }$$C� described by fractional-order differential equations. A method for determining the current and voltage waveforms in the analyzed circuit, based on the decomposition of rational functions into partial fractions, has been described. This method allows to determine transient waveform shapes in the system for any kind of voltage excitation. Two cases of the problem solutions have been considered. The first case concerns a situation where poles of rational functions are real, and the second where rational functions have complex poles. Effective relations enabling the determination of transient waveforms in a closed form have been given. Analytical formulae describing transient state waveforms in the system for different types of voltage excitations: constant, monoharmonic, periodic and arbitrary being an element of a Hilbert space, have been determined, too. The obtained results have been illustrated by an example.

Journal ArticleDOI
TL;DR: An effective detection algorithm is proposed to identify single source points where only one source occurs and a method based on probability density is proposed in order to find more reliable single sources points and cluster them.
Abstract: This paper considers mixing matrix estimation for underdetermined blind source separation. First, we propose an effective detection algorithm to identify single source points where only one source occurs. The detection algorithm finds single source points by utilizing the time---frequency coefficients of mixed signals and the complex conjugates of the coefficients. Then, a method based on probability density is proposed in order to find more reliable single source points and cluster them. Finally, the mixing matrix is obtained through re-selecting and clustering single source points. The experimental results indicate that the algorithm can accurately estimate the mixing matrix when there are fewer sensors than sources.

Journal ArticleDOI
TL;DR: Experimental results show that the proposed DWT–RDM approach renders a near-zero objective difference grade in the perceptual evaluation of audio quality even when the signal-to-noise ratio maintains at a level near 20 dB.
Abstract: A scheme jointly exploring the rational dither modulation (RDM) and auditory masking properties in the discrete wavelet transform (DWT) domain is proposed to achieve effective blind audio watermarking. The embedding of binary information is carried out by modulating coefficient vectors in the 5th-level approximation subband using the quantization steps estimated from past watermarked vectors. The robustness and payload capacity of the proposed scheme are maneuverable by varying vector dimensions, while the imperceptibility is ensured by constraining quantization noise below the auditory masking threshold. Furthermore, the periodic characteristic inherited in the RDM formulation can be used to re-establish synchronization for accurate watermark extraction. Experimental results show that the proposed DWT---RDM approach renders a near-zero objective difference grade in the perceptual evaluation of audio quality even when the signal-to-noise ratio maintains at a level near 20 dB. In most digital signal processing attacks, the bit error rates of retrieved watermarks are sufficiently low as compared to other recently developed methods with fewer payload capacities.

Journal ArticleDOI
TL;DR: A reduced-order observer is introduced to estimate the unmeasurable states of the switched system and an appropriate stochastic Lyapunov–Krasovskii functional deals with the time-delay terms, and fuzzy logic systems are employed to approximate the unknown nonlinearities.
Abstract: In this paper, a design scheme for an adaptive fuzzy tracking controller is proposed for a class of switched stochastic nonlinear time-delay systems via dynamic output-feedback. First, a reduced-order observer is introduced to estimate the unmeasurable states of the switched system. During the adaptive controller design procedure, an appropriate stochastic Lyapunov---Krasovskii functional deals with the time-delay terms, and fuzzy logic systems are employed to approximate the unknown nonlinearities. Based on the designed controller, the semi-globally uniform ultimate boundedness of all the closed-loop signals is guaranteed and the tracking error converges to a small neighborhood of the origin. Finally, a simulation example is given to illustrate the validity of the proposed approach.