On FIR Filter Approximation of Fractional-Order Differentiators and Integrators

Johansson, Håkan

doi:10.1109/jetcas.2013.2273853

Cited by 18 publications

(7 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where the filter coefficients are polynomial functions in parameter : (22) Substituting (22) into (21), the transfer function is rewritten as (23) where sub-filters . The design problem of variable FOD is how to determine filter coefficients such that the frequency response approximates the ideal response as well as possible.…”

Section: Designs Of Variable Generalized Fod and Foimentioning

confidence: 99%

“…The FOD design problem is how to find a digital filter such that its actual frequency response fits the ideal response as well as possible. When the order is fixed, it is called the fixed fractional order differentiator (FFOD) design [9]- [12], [23]. Some typical methods to design FFOD are Taylor series expansion method, continued fraction expansion method, radial basis function method and discrete cosine trans- form method.…”

Section: Introductionmentioning

confidence: 99%

“…Because the magnitude response of generalized FOD is controlled by parameter and phase response is controlled by parameter , an FOD design with independent control of magnitude and phase responses can be obtained. On the other hand, some methods have been also presented to design fractional order integrator (FOI) such that the fractional order integrals of digital signals can be computed [15], [23]. The ideal frequency response of FOI is given by (4) To let magnitude and phase of FOI be controlled independently, the above ideal frequency response of FOI is generalized to the following response (5) Another purpose of this paper is to study the design of the generalized FOI defined in (5).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Designs of Discrete-Time Generalized Fractional Order Differentiator, Integrator and Hilbert Transformer

Tseng

Lee

2015

IEEE Trans. Circuits Syst. I

View full text Add to dashboard Cite

In this paper, the design of a generalized fractional order differentiator (FOD) whose magnitude and phase responses can be controlled independently is investigated. First, a relation between conventional FOD and generalized FOD is studied such that the design tools of conventional FOD in the literature can be used to design variable generalized FOD directly. Then, the similar method is applied to design generalized fractional order integrator (FOI). Next, the proposed generalized FOD and FOI are used to generate a secure single side band (SSB) signal for saving the transmission bandwidth. The parameters of variable generalized FOD and FOI can be used as the secure keys for construction and reconstruction. Finally, the relation between fractional Hilbert transformer and generalized FOD is studied and the edge detection application is demonstrated to show the flexibility and effectiveness of the proposed generalized FOD.Index Terms-Fractional calculus, fractional Hilbert transformer, fractional order differentiator, fractional order integrator, single side band. 1549-8328

show abstract

Section: Designs Of Variable Generalized Fod and Foimentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Designs of Discrete-Time Generalized Fractional Order Differentiator, Integrator and Hilbert Transformer

Tseng

Lee

2015

IEEE Trans. Circuits Syst. I

View full text Add to dashboard Cite

show abstract

“…Many authors [17][18][19][20] gave techniques for IIR integrators with techniques like backward integrator, low orders approximation avoiding fractional delays, group delay compensation based on Taylor series, presenting compact formula related to the length of the filter using Lagrange interpolators, etc. Mathematical formula to calculate weights for the specified filter design, related to order [21][22][23][24] lead to the implementation of the digital integrators popularly.…”

Section: Introductionmentioning

confidence: 99%

Approximation and Analysis of Single Band FIR Pass Integrator Centered around Mid-band Frequencies with Degree k = 1, 2, 3…

Bhardwaj¹,

Kumar²,

Yadava³

2020

Period. Polytech. Elec. Eng. Comp. Sci.

View full text Add to dashboard Cite

In this paper, a modified Finite Impulse Response based linear Pass integrator for centered frequency, ranging between 0.1 π to 0.9 π has been realized. Both the cases have been considered i.e. for what values the phase response is of use and where the phase response has zero value. An iterative formula has been used to calculate the weights depending upon the Transfer Functions, and applying differentiation method. A flat output approximation for the desired frequency ω has been applied for which the results overlap with the ideal integrator. Performance comparison of the proposed integrator has been done with the previous one and relative percentage errors have been observed for both cases implemented. Graphical analysis has also been carried out for frequency responses having degree greater than one (i.e. k = 2, 3, 4) for both cases of proposed integrator and compared with the ideal integrator's response.

show abstract

“…As compared to IIR filters, FIR filters have no constraint on maximum sampling rate and they are always stable. 30 Experimentation plays an important role in learning and research. 31 Fractional systems can be implemented using a microcontroller, digital signal processor (DSP), field-programmable gate array (FPGA), etc.…”

Section: Introductionmentioning

confidence: 99%

Unique fractional calculus engineering laboratory for learning and research

Khubalkar

Junghare

Aware

et al. 2018

International Journal of Electrical Engineering & Education

View full text Add to dashboard Cite

In this paper, a novel prototype laboratory is presented for engineering education, in which experiments are based on the fractional calculus. The prototypes of analog and digital fractional-order proportional-integral-derivative (PID) controllers are built in the laboratory. These fractional-order PID controllers are applied to linear and nonlinear plants to demonstrate the effectiveness of fractional-order calculus in real time. These experiments are designed, developed, and implemented on the analog and digital platforms. These controllers are integrated to control the DC motor, brushless DC motor, and magnetic levitation modules through hardware-in-loop as well as stand-alone systems. The analog type of fractional-order PID implementation is carried out by using passive components (i.e. resistances and capacitances) with an operational amplifier. However, real-time digital implementation is carried out using field-programmable gate array and digital signal processor. This paper describes how the experiments on fractional calculus can be tailored for graduate, undergraduate students’ education and extended for research in this emerging area.

show abstract

On FIR Filter Approximation of Fractional-Order Differentiators and Integrators

Cited by 18 publications

References 29 publications

Designs of Discrete-Time Generalized Fractional Order Differentiator, Integrator and Hilbert Transformer

Designs of Discrete-Time Generalized Fractional Order Differentiator, Integrator and Hilbert Transformer

Approximation and Analysis of Single Band FIR Pass Integrator Centered around Mid-band Frequencies with Degree k = 1, 2, 3…

Unique fractional calculus engineering laboratory for learning and research

Contact Info

Product

Resources

About