2017
DOI: 10.1049/el.2016.3025
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Lowpass filters approximation based on modified Jacobi polynomials

Abstract: he orthogonal Jacobi polynomials are not suitable for use as the characteristic function in the continuous-and discrete-time filter design, because they are not fulfilling the basic condition: to be pure odd or pure even. A simple modification of Jacobi polynomials, is performed to obtain a new filter approximating function is proposed. Magnitude frequency responses of obtained filters exhibit more general behaviour compared with that of classical Gegenbauer (ultraspherical) filters, due to one additional para… Show more

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Cited by 3 publications
(3 citation statements)
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“…The magnitude‐squared characteristic function of a continuous‐time lowpass filter with m pairs of finite transmission zeros in the stopband can be written as An)(Ω2=i=1mnormalΩ2normalΩ0i22i=1mnormalΩ2normalΩ0i22+εp2λ2Jn(α,β)(Ω)21where λ=i=1m)(Ω0i21, Ω0i is i th zero position and Ω0i>1, n > 2 m denotes the filter degree, and εp is a passband edge ripple factor. The polynomial scriptJnfalse(α,βfalse)false(normalΩfalse)=1Cnfalse(α,βfalse)Pn(α,β)(Ω)+Pn(β,α)(Ω)is a modified Jacobi polynomials [1], generated by using the parity relation for Jacobi orthogonal polynomials Pnfalse(α,βfalse)false(normalΩ…”
Section: Approximationmentioning
confidence: 99%
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“…The magnitude‐squared characteristic function of a continuous‐time lowpass filter with m pairs of finite transmission zeros in the stopband can be written as An)(Ω2=i=1mnormalΩ2normalΩ0i22i=1mnormalΩ2normalΩ0i22+εp2λ2Jn(α,β)(Ω)21where λ=i=1m)(Ω0i21, Ω0i is i th zero position and Ω0i>1, n > 2 m denotes the filter degree, and εp is a passband edge ripple factor. The polynomial scriptJnfalse(α,βfalse)false(normalΩfalse)=1Cnfalse(α,βfalse)Pn(α,β)(Ω)+Pn(β,α)(Ω)is a modified Jacobi polynomials [1], generated by using the parity relation for Jacobi orthogonal polynomials Pnfalse(α,βfalse)false(normalΩ…”
Section: Approximationmentioning
confidence: 99%
“…Introduction: In the recently published paper [1], the authors have reported that the modified Jacobi polynomials can be used to construct a useful allpole lowpass filter functions. For the given lowpass filter degree, two parameters of the modified Jacobi polynomial can be used to a trade-off between passband magnitude response having ripples or being nearly monotonic, transition band width, or group delay deviation in the passband [2].…”
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confidence: 99%
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