A convex optimization method to solve a filter design problem

Le, Thanh Hieu; Barel, Marc Van

doi:10.1016/j.cam.2013.04.044

Cited by 5 publications

(5 citation statements)

References 9 publications

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“…From this order, the necessary coefficients can be determined through provided design equations or from tables of available coefficients, which are further used in the implementation and realization of the necessary circuits. Additionally, optimization methods have also been explored to design these types of circuits [22,23].…”

Section: Coefficient Determinationmentioning

confidence: 99%

Validation of Fractional-Order Lowpass Elliptic Responses of (1 + α)-Order Analog Filters

et al. 2018

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In this paper, fractional-order transfer functions to approximate the passband and stopband ripple characteristics of a second-order elliptic lowpass filter are designed and validated. The necessary coefficients for these transfer functions are determined through the application of a least squares fitting process. These fittings are applied to symmetrical and asymmetrical frequency ranges to evaluate how the selected approximated frequency band impacts the determined coefficients using this process and the transfer function magnitude characteristics. MATLAB simulations of ( 1 + α ) order lowpass magnitude responses are given as examples with fractional steps from α = 0.1 to α = 0.9 and compared to the second-order elliptic response. Further, MATLAB simulations of the ( 1 + α ) = 1.25 and 1.75 using all sets of coefficients are given as examples to highlight their differences. Finally, the fractional-order filter responses were validated using both SPICE simulations and experimental results using two operational amplifier topologies realized with approximated fractional-order capacitors for ( 1 + α ) = 1.2 and 1.8 order filters.

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Section: Coefficient Determinationmentioning

confidence: 99%

Validation of Fractional-Order Lowpass Elliptic Responses of (1 + α)-Order Analog Filters

et al. 2018

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“…Note that in (14), some of the parameters y αi and x αi are zero (corresponding to the strictly upper triangular part of G). Set…”

Section: Thanh Hieu Le and Marc Van Barelmentioning

confidence: 99%

“…defined by (14). Since for any g(z) ∈ Σ (n, d) there exist two real matrices X, Y so that (13) is satisfied, Σ (n, d) is isomorphic to a subset of Im(Φ).…”

Section: Proposition 7 [6]mentioning

confidence: 99%

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On bounds of the Pythagoras number of the sum of square magnitudes of Laurent polynomials

Barel

2016

NACO

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This paper presents a lower and upper bound of the Pythagoras number of sum of square magnitudes of Laurent polynomials (sosm-polynomials). To prove these bounds, properties of the corresponding system of quadratic polynomial equations are used. Applying this method, a new proof for the best (known until now) upper bound of the Pythagoras number of real polynomials is also presented.2010 Mathematics Subject Classification. Primary: 11E25, 12Y05; Secondary: 65H10. Key words and phrases. Pythagoras number, sum of squares, sum of square magnitudes of Laurent polynomials.

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“…The game theoretic approaches, such as Stackelberg game [21], are used to achieve the equilibrium state (e.g., Nash equilibrium [22]) and it involves PUs and SUs as players of the game. Examples of the nongame theoretic approaches are reinforcement learning [23] and convex optimization [24]. Table 1 presents the gains, functions, and characteristics of the spectrum leasing schemes.…”

Section: Spectrum Leasing Schemes In Cognitive Radio Networkmentioning

confidence: 99%

Spectrum Leasing in Cognitive Radio Networks: A Survey

Syed

Yau

2014

International Journal of Distributed Sensor Networks

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Cognitive Radio (CR) is a dynamic spectrum access approach, in which unlicensed users (or secondary users, SUs) exploit the underutilized channels (or white spaces) owned by the licensed users (or primary users, PUs). Traditionally, SUs are oblivious to PUs, and therefore the acquisition of white spaces is not guaranteed. Hence, a SU must vacate its channel whenever a PU reappears on it in an unpredictable manner, which may affect the SUs' network performance. Spectrum leasing has been proposed to tackle the aforementioned problem through negotiation between the PU and SU networks, which allows the SUs to acquire white spaces for a guaranteed period of time. Through spectrum leasing, the PUs and SUs enhance their network performances, and additionally PUs maximize their respective monetary gains.

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A convex optimization method to solve a filter design problem

Cited by 5 publications

References 9 publications

Validation of Fractional-Order Lowpass Elliptic Responses of (1 + α)-Order Analog Filters

Validation of Fractional-Order Lowpass Elliptic Responses of (1 + α)-Order Analog Filters

On bounds of the Pythagoras number of the sum of square magnitudes of Laurent polynomials

Spectrum Leasing in Cognitive Radio Networks: A Survey

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