Grobner Basis Design of Incomplete Chebyshev Polynomials

   Ivan W. Selesnick  
   Department of Electrical and Computer Engineering - MS 366 
   Rice University, Houston, TX 77251-1892, USA 
   selesi@ece.rice.edu
   http://www-dsp.rice.edu/

This paper describes a novel technique using Grobner bases for 
constructing monic polynomials of the form x^k P(x) that best 
approximate 0 in the Chebyshev sense, an approximation problem 
discussed by Souto in his 1970 dissertation on filter design.
In this paper, a differential equation in two polynomials is 
given and it is suggested that a Grobner basis be used to obtain
the sought coefficients.  The resulting polynomials can be used 
to design analogue and digital IIR filters the properties of 
which are between those of the classical Butterworth and 
Chebyshev filters of types I and II.