# 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} }

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

#### 30 Citations

New windows family based on modified Legendre polynomials

- 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. Deczky… Expand

Design of Nonrecursive Digital Filters Using the Ultraspherical Window Function

- Mathematics, Computer Science
- EURASIP J. Adv. Signal Process.
- 2005

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

- Mathematics
- 2013

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… Expand

New compactly supported scaling and wavelet functions derived from Gegenbauer polynomials

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

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 to… Expand

Generation of ultraspherical window functions

- Computer Science, Mathematics
- 2002 11th European Signal Processing Conference
- 2002

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

- Mathematics
- 2011

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 becomes… Expand

Design of Ultraspherical Window Functions with Prescribed Spectral Characteristics

- Mathematics, Computer Science
- EURASIP J. Adv. Signal Process.
- 2004

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

- Mathematics
- 2012

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 optimal… Expand

Nonrecursive digital filter design using the ultraspherical window

- 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 of… Expand

All-Pole Recursive Digital Filters Design Based on Ultraspherical Polynomials

- Mathematics
- 2014

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, is… Expand

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