On designing FIR filters using windows based on Gegenbauer polynomials

Rowinska-Schwarzweller, A.; Wintermantel, M.

doi:10.1109/iscas.2002.1009865

Cited by 6 publications

(4 citation statements)

References 3 publications

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“…the main lobe and sidelobes' peak as for unispherical windows [6]. This family of windows is based on Gegenbauer polynomials [7], being the generalization of Legendre polynomials and the special cases of Jacobi polynomials.…”

Section: Window Functions and Their Parametersmentioning

confidence: 99%

“…The overall computational complexity of such window is equal to N+M+2 operations (N and M arithmetic operations for both polynomials, 1 for the substitution and one for the division of both polynomials). In such sense the application of such defined rational polynomial window instead of the polynomial window (7) leads to lower computational complexity if N+M is less than the order of polynomial window (7) or the half of the order of polynomial used for the expansion into series (the computational complexity of the "full" polynomial of N-th order, with all exponents, is equal to 2•N operations). Nevertheless, using the rational functions a better fitting of window function to the "ideal" shape of the window is possible.…”

Section: Proposed Family Of Rational Polynomial Windows and Their Ene...mentioning

confidence: 99%

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Rational Polynomial Windows as an Alternative for Kaiser Window

Okarma

2012

ElAEE

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Section: Window Functions and Their Parametersmentioning

confidence: 99%

Section: Proposed Family Of Rational Polynomial Windows and Their Ene...mentioning

confidence: 99%

Rational Polynomial Windows as an Alternative for Kaiser Window

Okarma

2012

ElAEE

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“…None of those windows is optimized towards low sidelobes level, since e.g. window presented in the paper [8] is based on the minimization of the energetic criterion, similarly as Kaiser window, and the recently proposed modification of Hamming window [7] is still based on the raised-cosine windows family.…”

Section: Introductionmentioning

confidence: 99%

Constructed Polynomial Windows with High Attenuation of Sidelobes

Okarma

2013

ElAEE

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In the paper the idea of the constructed polynomial windows is presented together with the obtained results of their optimization towards low level of the sidelobes. The main advantages of the polynomial windows are their low computational complexity and ability to change their frequency properties by some modifications of the polynomial coefficients in the time domain. Both of these merits are preserved in the constructed polynomial windows family discussed in the paper and the additional profit is the possibility of using two lower order polynomials with additional switching operation with similar sidelobes' attenuation as for higher order standard polynomial windows.

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“…Gegenbauer polynomials have already been used in lowpass and high-pass filter design [2][3][4][5]. In both cases, these polynomials have been associated to frequency response of those filters for window and wavelet design.…”

Section: Introductionmentioning

confidence: 99%

New compactly supported scaling and wavelet functions derived from Gegenbauer polynomials

Soares

Oliveira

Cintra

Canadian Conference on Electrical and Computer Engineering 2004 (IEEE Cat. No.04CH37513)

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A new family of scaling and wavelet functions is introduced, which is derived from Gegenbauer polynomials. The association of ordinary second order differential equations to multiresolution filters is employed to construct these new functions. These functions, termed ultraspherical harmonic or Gegenbauer scaling and wavelet functions, possess compact support and generalized linear phase. This is an interesting property since, from the computational point of view, only half the number of filter coefficients are required to be computed. By using an alpha factor that is within the orthogonality range of such polynomials, there are generated scaling and wavelet that are frequency selective FIR filters. Potential application of such wavelets includes fault detection in transmission lines of power systems.

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On designing FIR filters using windows based on Gegenbauer polynomials

Cited by 6 publications

References 3 publications

Rational Polynomial Windows as an Alternative for Kaiser Window

Rational Polynomial Windows as an Alternative for Kaiser Window

Constructed Polynomial Windows with High Attenuation of Sidelobes

New compactly supported scaling and wavelet functions derived from Gegenbauer polynomials

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