Digital Differentiators Research Articles

Optimal wideband digital fractional-order differentiators using gradient based optimizer

In this paper, we propose a novel optimization approach to designing wideband infinite impulse response (IIR) digital fractional order differentiators (DFODs) with improved accuracy at low frequency bands. In the new method, the objective function is formulated as an optimization problem with two tuning parameters to control the error distribution over frequencies. The gradient based optimizer (GBO) is effectively employed on the proposed objective function. A wide range of design examples are presented to illustrate the effectiveness of the proposed approach. The proposed approximations are compared to those of recent literature in terms magnitude, phase, and group delay errors. The result reveal that our method can attain approximations have a favorable low frequency performance (with about 60% of relative magnitude error reduction) and maintain a comparable accuracy at most of the Nyquist band to those of the existing ones. Thus, our approximations can be attractive for low frequency applications.

A Real-Valued Kalman Estimation Method for Harmonic Signal Analysis in Biomedical Applications

This work presents a methodology for obtaining the harmonic estimation of biomedical signals such as electrocardiogram, cardiorespiratory and blood pressure signals. The proposed methodology is achieved using polynomial approximation and the Kalman filter. As advantage, the technique includes instant estimations of signal harmonics and its derivatives using a real-valued model. Furthermore, a comparison of the results is conducted with the Savitzky-Gola, nonlinear tracking differentiator methods, extended state observer and digital differentiator base on Taylor series. The results suggest that the proposed method has the potential to enhance the quality of signal measurements, especially in the presence of noise.

Design of Small-Phase Time-Variant Low-pass Digital Fractional Differentiators and Integrators

The design method and the time-variant FIR architecture for real-time estimation of fractional and integer differentials and integrals are presented in this paper. The proposed FIR architecture is divided into two parts. Small-phase filtering, integer differentiation, and fractional differential and integration on the local data are performed by the first part, which is time-invariant. The second part, which is time-variant, handles fractional and global differentiation and integration. The separation of the two parts is necessary because real-time matrix inversion or an extensive analytical solution, which can be computationally intensive for high-order FIR architectures, would be required by a single time-variant FIR architecture. However, matrix inversion is used in the design method to achieve negligible delay in the filtered, differentiated, and integrated signals. The optimum output obtained by the method of least squares results in the negligible delay. The experimental results show that fractional and integer differentiation and integration can be performed by the proposed solution, although the fractional differentiation and integration process is sensitive to the noise and limited resolution of the measurements. In systems that require closed-loop control, disturbance observation, and real-time identification of model parameters, this solution can be implemented.

A Low Power R-peak Detector Clocked at Signal Sampling Rate

This paper presents a real-time, low-power R-peak detector implemented in an FPGA. It is different from other implementations as it runs at the same signal sampling rate, rather than utilizing a high clock frequency as utilized in batch processing with high throughput systems. Such implementation relies on a Savitzky-Golay filter for power line noise filtering, and on an adapted version of the Difference Operation Method (DOM) algorithm. The modification in DOM is needed in order to be able to process the data either without increasing the clock to process data in a batch fashion or unsustainably increasing latency. It uses the Savitzky-Golay Digital Differentiator, eliminating further filtering stages. The prototype was characterized using both the MIT-BIH database and Fluke Prosim 8 Vital Signal Simulator. The proposed system features a high degree of matched R-peaks even being extremely efficient regarding power dissipation. Moreover, it shows similar performance when compared to the original Difference Operation Method implementation.The whole system consumes 260- uW operating at 192-Hz in an FPGA model 10M50DAF484C7G, which belongs to the MAX10 family of Altera devices.

Design of IIR full-band differentiators with improved nearly linear phase

Linear, or almost linear phase in the design of digital differentiators depends both on the method of calculation of the filter coefficients and the adopted structural design. Acknowledging the importance of this design objective, we developed a method to derive infinite impulse response differentiators which tackles it from both perspectives and yields improved characteristics compared to our previous design. We have replaced the differentiator structure comprising an all-pass filter and a delay line with a configuration of two infinite impulse response all-pass filters. Furthermore, we provide a procedure for determining an improved initial solution to the optimization of filter coefficients, as well as a procedure for improving the differentiator's magnitude response. The final solution exhibits considerably lower error at low frequencies and is thus suitable for the common scenario where the relevant spectral content decreases with frequency. The proposed filters of third and fifth order outperform many existing solutions in literature, especially in terms of the phase characteristic and time-domain performance.

Design and Applications of Digital Differentiators Using Model Order Reduction Techniques

A model order reduction technique is employed to design novel digital differentiators. The new mapping technique from s domain to z domain conversion is investigated in this paper. The differentiators under consideration are second order one viz. Simpsons and Tick differentiators. The novel transfer functions obtained by the model order reduction technique can be used in many signal processing, Image processing applications. As an example, edge detection application is illustrated.

Unified Filter Order Estimate for Minimax-Designed Linear-Phase FIR Wideband and Lowpass Digital Differentiators

Digital differentiators enable the computation of the derivative of a continuous-time signal at discrete time instances, and they are used in many signal processing applications. This paper derives a unified filter order estimate for digital differentiators that are realized with linear-phase finite-length impulse response filters and designed in the minimax sense. The estimate is useful at the high-level system design when assessing the implementation complexity and it enables fewer designs when finding the minimal filter order required to satisfy a prescribed tolerable approximation error. The proposed unified estimate covers both wideband and lowpass differentiators of integer degrees up to ten. Furthermore, degree-individual filter order estimates are derived which improve and extend previous results. The performance of both the unified and degree-individual order estimates is evaluated through simulation examples and compared with previous estimates.

A Low-Noise Int-Diff Small Direct Currents Measurement System With Two-Stage Amplifier and Digital Differentiator

A Low-Noise Int-Diff Small Direct Currents Measurement System With Two-Stage Amplifier and Digital Differentiator

Calibration of frequency response mismatches in time‐interleaved analog‐to‐digital converter based on adaptive method

AbstractThe time‐interleaved analog‐to‐digital converter (TIADC) system could achieve high sampling rate effectively, but the frequency response inconsistency among channels will introduce frequency response mismatches, which will seriously degrade the signal quality. In this paper, a novel multi‐channel frequency response mismatches adaptive calibration method is proposed. The frequency response of the compensation filter is expanded into a polynomial of a digital differentiator, and the least mean square adaptive strategy is used to calibrate frequency response mismatches. It does not require measuring the channel frequency responses in advance and uses digital post‐processing technology to effectively compensate the frequency response of the multi‐channel TIADC system and improve the spurious‐free dynamic range. The experimental results verify the effectiveness of the algorithm.

ВИЗНАЧЕННЯ ПАРАМЕТРІВ ТИПОВИХ ЦИФРОВИХ СТАТИЧНИХ РЕГУЛЯТОРІВ ПРОМИСЛОВИХ ЕЛЕКТРОПРИВОДІВ

The paper is devoted to the development of an analytical method for determining the settings of typical digital static regulators of industrial electric drives, which can be represented as discrete transfer functions in the Z-transform. It is offered to define parameters of adjustment of static regulators, proceeding from the set static error (statism). The possibility of technical realization of the digital proportional-differential regulator with an ideal digital differentiator is substantiated. Significant improvement of system performance indexes when using the differential component of a digital static controller is shown. References 10, figures 7.

Closed Form Approach for Constrained Design of nth-Order IIR Digital Differentiator

Closed Form Approach for Constrained Design of nth-Order IIR Digital Differentiator

A Control Strategy of LCL-Type Grid-Connected Inverters for Improving the Stability and Harmonic Suppression Capability

The conventional inverter-side current single-loop feedback control scheme is weak in suppressing the grid-side current harmonics, posing a challenge for an inverter to inject high-quality current under distorted grid voltage. With capacitor current compensation added, the control scheme achieves controllability of the grid-side current harmonics so that it can effectively suppress some specific harmonic components. However, due to the stability requirements, only a few low-order harmonic resonance controllers can be applied, which limits the mitigation of high-order harmonics. To tackle this problem, the grid-side current feedback control with inductor–capacitor–inductor (LCL) resonance damping is proposed in this paper. In this case, a higher LCL resonance frequency can be set compared to the inverter-side current single-loop feedback control scheme. Thereby, more resonance controllers can be applied to suppress high-order grid-side current harmonics. The active damping method of capacitor current proportional feedback plus capacitor voltage proportional feedback is adopted because of its high robustness to grid impedance variations. Furthermore, this paper reveals that the applied active damping method has a limitation in that it only considers a single inverter under inductive grid impedance, which cannot eliminate the risk of resonance caused by the interaction of multiple inverters and the grid. To address this issue, a phase lead compensator (PLC) is proposed, eliminating the resonance risk by removing the non-passive region of the inverter output admittance. To retain the advantage of the inverter-side current single-loop feedback control scheme, i.e., only a few measuring devices are required, a digital differentiator is used to calculate the capacitor current from the capacitor voltage. The difference between the measured inverter-side current and the calculated capacitor current is taken to approximate the grid-side current for the feedback control. The control performance is comparable to using the grid-side current for feedback. Simulation and experimental results demonstrate that the proposed control scheme endows the inverter with good stability and current quality without extra measurement devices.

Discrete cosine transform interpolation based design of two-dimensional FIR fractional order digital differentiator

Discrete cosine transform interpolation based design of two-dimensional FIR fractional order digital differentiator

Optimal design and low noise realization of digital differentiator

Abstract This manuscript presents a design of a differentiator in the digital domain with its low noise realization. It manifests the minimization of the L1 -error objective function by using a hybrid optimization technique consisting of the particle swarm and simulated annealing optimization algorithm. The obtained magnitude response provides a noteworthy approximation of the ideal differentiator with a minimal magnitude inaccuracy when compared with the existing designs. The realization structures are also investigated and compared in terms of the noise gain behavior.

$$L_1$$-Norm-Based Optimal Design of Digital Differentiator Using Multiverse Optimization

$$L_1$$-Norm-Based Optimal Design of Digital Differentiator Using Multiverse Optimization

Design and Optimization of Infinite Impulse Response Full-Band Digital Differentiator Using Evolutionary and Swarm Intelligence Algorithms

In this paper, the design and optimization of infinite impulse response full-band digital differentiator (DD) using evolutionary and swarm intelligence algorithms is investigated. Different objective functions based on the absolute error, the squared absolute error and the min-max optimality criterion are investigated. The optimal DD parameters that result in the best minimum value of the investigated objective functions are obtained using differential evolution, particle swarm optimization, genetic algorithm and cuckoo search optimization methods. These algorithms are used due to their simplicity, efficiency and robustness in solving general multidimensional optimization problems. The investigation outcomes show that minimizing the absolute error gives the most flat magnitude response, and minimizing the squared absolute error gives almost the lowest mean error of the designed DD. In addition, a new objective function is proposed to improve the linearity of the phase response of the designed infinite impulse response full-band DD. It is found that the design of the DD using the differential evolution outperforms or at least is comparable to similar designs reported in the literature using other optimization methods.

Design and Optimization of Enhanced Magnitude and Phase Response IIR Full-Band Digital Differentiator and Integrator Using the Cuckoo Search Algorithm

Design of full-band infinite impulse response (IIR) digital differentiator (DD) and digital integrator (DI) based on the L_k-norm and the min-max optimality criteria have been demonstrated in literature. However, the designed IIR DDs and DIs using these criteria do not have linear phase or have unsatisfactory magnitude response. In this paper, a novel approach to design, optimize and improve the magnitude response and the linearity of the phase response of IIR DD and DI using the cuckoo search (CS) optimization algorithm is proposed. The proposed approach is based on a varied L_<i>k</i>-norm where <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> linearly increases with the number of the frequency samples between the values 1 and 2. The design and optimization of DDs and DIs are carried out using the CS optimization method due to its simplicity, efficiency, and robustness in solving general multidimensional optimization problems. The performance of the designed DDs and DIs using the proposed approach is compared with designs based on different criteria and algorithms available in literature. The comparison shows that the designed DDs and DIs based on the proposed approach have better phase responses and better or at least comparable magnitude responses compared to those of DDs and DIs designed using other methods in the literature.

Guided Filtering Based Efficient Digital Differentiator Design for Electrocardiogram Signal Processing

Guided Filtering Based Efficient Digital Differentiator Design for Electrocardiogram Signal Processing

Intra and inter-patient arrhythmia classification using feature fusion with novel feature set based on fractional-order and fibonacci series

Cardiac ailments are increasing at an alarming rate globally due to the sedentary lifestyle and increased desk-bound activities. For decades, the ECG signal is used in aiding the analysis of human heart. Arrhythmia is a disorder that alters the normal cardiac cycle of ECG signal. The automatic classification of arrhythmia is a highly desirable and tough task. Mainly, the traditional methods of arrhythmia classification, are evaluated on the intra-patient criterion that may not befit the inter-patient criterion. A complete classification method has been proposed in the paper which performs well in intra-patient, inter-patient criterion and it is effective for minority class of MIT-BIH arrhythmia database (MIT-BIH-AD). In the proposed method, after preliminary processing based on Riesz fractional-order digital differentiator and R-peak detection, various features are extracted from ECG beat. The feature set proposed is a fusion of time-domain, time–frequency domain features and the new and novel features based on the Fibonacci series and coefficients of fractional-order Riesz based derivative signals which are proposed in this work. The results are evaluated on the MIT-BIH-AD and the results for intra-patients’ criterion have achieved an overall accuracy, sensitivity and positive predictivity values of 99.85%, 99.16%, 99.93% respectively, and for the inter-patient scheme 92.5%, 89.89% and 95.54% an average value of accuracy, sensitivity and positive predictivity of six ECG classes. The obtained results in both criterions have outperformed other methods in the literature and the proposed work has also attained better results for minority class of MIT-BIH-AD in both the scheme.

Design of low‐pass and band‐pass infinite impulse response maximally flat stable digital differentiators

Maximally flat digital differentiators (MFDDs) are very attractive for differentiation of narrowband signals. The design of infinite impulse response (IIR) MFDDs, however, is very challenging due to the non-convexity of the flatness constraints of the IIR digital differentiator (DD). This study derives a set of linear conditions that are equivalent to the non-convex flatness constraints and then utilises these conditions to design low-pass and band-pass IIR MFDDs with low and nearly constant group delay. In addition, a generalized-positive-realness-based stability constraint is incorporated in the design to ensure the robust stability of the DD. A design algorithm is presented to maximise the total flatness degree subject to the flatness conditions and the stability constraint, resulting in maximally flat stable DDs (MFSDDs). Design examples and comparisons with existing DDs demonstrate that the designed IIR MFSDDs have better magnitude and group-delay responses and lower implementation complexity.