Unispherical windows

@article{Deczky2001UnisphericalW,
  title={Unispherical windows},
  author={A. G. Deczky},
  journal={ISCAS 2001. The 2001 IEEE International Symposium on Circuits and Systems (Cat. No.01CH37196)},
  year={2001},
  volume={2},
  pages={85-88 vol. 2}
}
  • A. Deczky
  • Published 2001
  • Mathematics, Computer Science
  • ISCAS 2001. The 2001 IEEE International Symposium on Circuits and Systems (Cat. No.01CH37196)
In this paper the author discusses a new class of window functions based on the orthogonal polynomials known as the Gegenbauer or ultraspherical polynomials. These functions have a close relationship with the Jacobi polynomials and with the well known Chebyshev polynomials which are a special case. The window functions derived from these polynomials have the interesting property that the rolloff of the sidelobes with frequency is controlled by a parameter, leading to the design of a whole class… Expand
New windows family based on modified Legendre polynomials
  • M. Jaskula
  • Mathematics
  • IMTC/2002. Proceedings of the 19th IEEE Instrumentation and Measurement Technology Conference (IEEE Cat. No.00CH37276)
  • 2002
In this paper we comparing a new class of window functions based on the orthogonal polynomials known as the Legendre Polynomials and a standard Blackman and Hamming windows. Recently, A.G. DeczkyExpand
Design of Nonrecursive Digital Filters Using the Ultraspherical Window Function
TLDR
Experimental results demonstrate that in many cases the ultraspherical window yields a lower-order filter relative to designs obtained using windows like the Kaiser, Dolph-Chebyshev, and Saramäki windows. Expand
Constructed Polynomial Windows with High Attenuation of Sidelobes
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 theExpand
New compactly supported scaling and wavelet functions derived from Gegenbauer polynomials
A new family of scaling and wavelet functions is introduced; it is derived from Gegenbauer polynomials. The link of ordinary 2nd order differential equations to multiresolution filters is employed toExpand
Generation of ultraspherical window functions
TLDR
Two methods for the computation of the coefficients of the ultrasp spherical window are presented and a new method that involves equating an ultraspherical window's frequency-domain representation to a Fourier series from which the coefficients are readily found is presented. Expand
Analysis of Novel Window Based on the Polynomial Functions
A simple form of a window function with application to FIR filter design is implemented two parts, that is using polynomial functions with grade two and three and computational complexity becomesExpand
Design of Ultraspherical Window Functions with Prescribed Spectral Characteristics
TLDR
A comparison with other windows has shown that a difference in performance exists between the ultraspherical and Kaiser windows, which depends critically on the required specifications. Expand
Rational Polynomial Windows as an Alternative for Kaiser Window
In the paper a new family of energetically optimized rational polynomial windows useful for signal processing applications is presented. A typical approximation of the energetically optimalExpand
Nonrecursive digital filter design using the ultraspherical window
  • Stuart W. A. Bergen, A. Antoniou
  • Mathematics
  • 2003 IEEE Pacific Rim Conference on Communications Computers and Signal Processing (PACRIM 2003) (Cat. No.03CH37490)
  • 2003
A method for the design of nonrecursive digital filters using the ultraspherical window is proposed. The method is based on empirical formulas for the filter length and the independent parameters ofExpand
All-Pole Recursive Digital Filters Design Based on Ultraspherical Polynomials
A simple method for approximation of all-pole recursive digital filters, directly in digital domain, is described. Transfer function of these filters, referred to as Ultraspherical filters, isExpand
...
1
2
3
...

References

SHOWING 1-3 OF 3 REFERENCES
MATLAB. The Lnriguage of Matl?eiiiatical Coriipirtirig
  • The Mathworks Inc,
  • 1975
Tlicor?, arid Applicatiori of' Digital Sigr id: P r~ocessirig
  • 1974
Haridbok of Matl?e~iiarical Furictioris, Dover Publications
  • N.Y
  • 1965