Inverse Ultraspherical Filters

Corral, C.A.

doi:10.1007/s10470-005-5750-4

Cited by 4 publications

(3 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Many of the before mentioned polynomials are special cases of modified Jacobi polynomials. Namely, Gegenbauer (symmetric Jacobi) [5], Chebyshev of first and second kind, Legendre and Chebyshev of third and fourth kind are obtained for

α = β

α = β = \pm 1 / 2

α = β = 0

and

α = - β = \pm 1 / 2

, respectively.…”

Section: Modified Jacobi Polynomialsmentioning

confidence: 99%

“…1, it is monotonically increasing for n even and for x , −1 it is monotonically decreasing for n odd.Many of the before mentioned polynomials are special cases of modified Jacobi polynomials. Namely, Gegenbauer (symmetric Jacobi)[5], Chebyshev of first and second kind, Legendre and Chebyshev of third and fourth kind are obtained for a = b, a = b = +1/2, a = b = 0 and a = −b = +1/2, respectively.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Lowpass filters approximation based on modified Jacobi polynomials

Stojanović

Stamenković²,

Krstić³

2017

Electron. lett.

View full text Add to dashboard Cite

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 parameter available in the Jacobi polynomials. This parameter can be used to obtain magnitude response with either smaller passband ripple values (nearly monotonic behaviour), smaller group delay variations or sharper cutoff slope. The proposed modified Jacobi polynomials are not orthogonal, however, many known orthogonal polynomials can be obtained as theirs special cases.

show abstract

α = β

α = β = \pm 1 / 2

α = β = 0

and

α = - β = \pm 1 / 2

, respectively.…”

Section: Modified Jacobi Polynomialsmentioning

confidence: 99%

mentioning

confidence: 99%

Lowpass filters approximation based on modified Jacobi polynomials

Stojanović

Stamenković²,

Krstić³

2017

Electron. lett.

View full text Add to dashboard Cite

show abstract

α = β

α = β = \pm 1 / 2

α = β = 0

and

α = - β = \pm 1 / 2

, respectively.…”

Section: Modified Jacobi Polynomialsmentioning

confidence: 99%

Lowpass filters approximation based on modified Jacobi polynomials

Stojanović

Stamenković²,

Krstić³

2017

Electron. lett.

View full text Add to dashboard Cite

he orthogonal Jacobi polynomials are not suitable for the characteristic function in the continuous-and discrete-time filter designs because they are not fulfilling the basic conditions: to be pure odd or to be pure even. A simple modification of Jacobi polynomials, proposed in this Letter, is performed to obtain a new filter approximating function. Magnitude frequency responses of obtained filters exhibit more general behaviour compared to that of classical Gegenbauer (ultraspherical) filters, due to one additional parameter available in the Jacobi polynomials. This parameter can be used to obtain magnitude response with smaller passband ripple values (nearly monotonic behaviour), smaller group delay variations or sharper cutoff slope. The proposed modified Jacobi polynomials are not orthogonal; however, many known orthogonal polynomials can be obtained as theirs special cases.

show abstract

Lowpass & Highpass Filter Characteristics

Self¹

2011

The Design of Active Crossovers

View full text Add to dashboard Cite

Inverse Ultraspherical Filters

Cited by 4 publications

References 16 publications

Lowpass filters approximation based on modified Jacobi polynomials

Lowpass filters approximation based on modified Jacobi polynomials

Lowpass filters approximation based on modified Jacobi polynomials

Lowpass & Highpass Filter Characteristics

Contact Info

Product

Resources

About