Title :
Least-squares design of higher order nonrecursive differentiators
Author :
Sunder, S. ; Ramachandran, Ravi P.
Author_Institution :
Dept. of Electr. & Comput. Eng., Concordia Univ., Montreal, Que., Canada
fDate :
4/1/1994 12:00:00 AM
Abstract :
A method is described that can be used to design non-recursive linear-phase higher order differentiators that can perform differentiation over any frequency range. The method is based on formulating the absolute mean-square error between the amplitude responses of the practical and ideal differentiator as a quadratic function. The coefficients of the differentiators are obtained by solving a set of linear equations. This method leads to a lower mean-square error and is computationally more efficient than both the eigenfilter method and the method based on the Remez exchange algorithm. Design of differentiators based on minimization of the relative mean-square error is also carried out. Finally, the method is extended to the design of frequency selective higher order differentiators
Keywords :
computational complexity; delay circuits; digital filters; filtering and prediction theory; frequency response; least squares approximations; signal processing; absolute mean-square error; amplitude responses; frequency range; frequency selective higher order differentiators; higher order nonrecursive differentiators; linear equations; minimization; quadratic function; relative mean-square error; Algorithm design and analysis; Design methodology; Differential equations; Eigenvalues and eigenfunctions; Filters; Frequency; Linear approximation; Minimax techniques; Signal processing; Signal processing algorithms;
Journal_Title :
Signal Processing, IEEE Transactions on
