The fractional-order derivative and integral of Grünwald Letnikov's definition are implemented based on FPGA for different fractional orders. A new algorithm is proposed to implement the GL integral based on linear approximation approach, where the memory dependency of the fractional order systems is eliminated. Moreover, the linear approximation design shows an improvement of 91% and 92% in the error and the mean percentage error compared with prior art. The proposed approach has been designed and implemented based on Verilog Hardware Description Language (HDL) and realized on Nexys 4 Artix-7

Exploring the use of fractional calculus is essential for it to be used properly in various applications. Implementing the fractional operator Dα in FPGA is an important research topic in fractional calculus; in the literature, only a few FPGA implementations have been proposed due to the memory dependence of the fractional order systems. In this paper, FPGA implementations of fractional order integrator/differentiator based on the Grünwald-Letnikov (GL) operator are proposed. Two algorithms are developed based on look-up table and quadratic and piece-wise linear approximation approaches to

This paper introduces two FPGA based design approaches of the fractional order integrator and differentiator using Grünwald Letnikov (GL) definition where fixed window and linear approximation approaches are considered. The main advantage of the linear approximation method is that it reduces the huge memory of the fractional order systems. One of the top applications of fractional calculus is the fractional order Proportional Integral Derivative (FOPID) controller. It has gained a great attention in academic studies and in industrial applications. The proposed approaches have been used as

This paper presents a study of fractional order oscillator design based on a matrix. The presented oscillator consists of a general two port network and three impedances. Only two port with single element in its transmission matrix is discussed which gives four possible networks. Different combinations for one element have been investigated. The impedances associated with the studied networks are series or parallel connection of resistors in addition to fractional order capacitors. The characteristic equation, oscillation frequency and condition for each combination are introduced. Numerical

In this paper, a general analysis of the fractional order operational transresistance amplifiers (OTRA) based oscillator is presented and validated through eight different circuits which represent two classifications according to the number of OTRAs. The general analytical formulas of the oscillation frequency, condition as well as the phase difference are illustrated for each case and summarized in tables. One of the advantages of the fractional-order circuit is the extra degrees of freedom added from the fractional-order parameters. Moreover different special cases {α = β ≢ 1, β ≢ α = 1, α ≢

This paper presents a comparative study of four fractional order filters used for edge detection. The noise performance of these filters is analyzed upon the addition of random Gaussian noise, as well as the addition of salt and pepper noise. The peak signal to noise ratio (PSNR) of the detected images is numerically compared. The mean square error (MSE) of the detected images as well as the execution time are also adopted as evaluation methods for comparison. The visual comparison of the filters capability in medical image edge detection is presented, that can help in the diagnosis of

This paper presents a secured highly sensitive image encryption system suitable for biomedical applications. The pseudo random number generator of the presented system is based on two discrete logistic maps. The employed maps are: the double humped logistic map as well as the fractional order logistic map. The mixing of the map parameters and the initial conditions x0, offers a great variety for constructing more efficient encryption keys. Different analyses are introduced to measure the performance of the proposed encryption system such as: histogram analysis, correlation coefficients, MAE

Pulsed wave Doppler ultrasound is commonly used in the diagnosis of cardiovascular and blood flow abnormalities. Doppler techniques have gained clinical significance due to its safety, real-time performance and affordability. This work presents the development of a pulsed wave spectral Doppler module, which was integrated into a reconfigurable ultrasound system. The targeted system adopts a hardware-software partitioning scheme where an FPGA handles the front-end and a PC performs the back-end. Two factors were considered during the design. First, the data transfer rate between hardware and

This paper presents a comparative study of edge detection algorithms based on integer and fractional order differentiation. A performance comparison of the two algorithms has been proposed. Then, a soft computing technique has been applied to both algorithms for better edge detection. From the simulations, it shows that better performance is obtained compared to the classical approach. The noise performances of those algorithms are analyzed upon the addition of random Gaussian noise, as well as the addition of salt and pepper noise. The performance has been compared to peak signal to noise

This paper presents a multiplierless based FPGA implementation for six different chaotic Pseudo Random Number Generators (PRNGs) that are based on: Chua, modified Lorenz, modified Rössler, Frequency Dependent Negative Resistor (FDNR) oscillator, and other two systems that are modelled using the simple jerk equation. These chosen systems can be employed in high speed applications because they don't utilize any hardware multiplier. The proposed PRNGs have been implemented using VHDL, synthesized on Xilinx, using the FPGA: XC5VLX50T, and tested using the NIST statistical suite. Furthermore, a