alpha-Spline design of finite impulse response digital filters

作者：Angel Raposo Sanchez Miguel; Saez Landete Jose; Cruz Roldan Fernando

来源：Signal Processing, 2016, 122: 204-212.

DOI：10.1016/j.sigpro.2015.12.010

• Convolution
• Discrete time systems
• Filtering theory and FIR digital filters
• Principally flat filters
• alpha-splines and beta-splines functions
• Optimization and genetic algorithm

The use of transition functions to connect the passband and the stopband in the ideal amplitude frequency response of an FIR filter reduces the oscillations near the band edges caused by the Gibbs phenomenon in filters designed by windowing. To this end, several methods based on beta-splines have been proposed, in which an integer order of the spline is used to properly shape the transition band of the filter. However, it has been reported in the literature that the optimal value of the spline order that minimizes the approximation's mean square error may take non-integer values. Therefore, there is a lack of a precise formulation that allows the use of real positive numbers to properly design spline based digital filters. The aim of this paper is to solve this problem, presenting a new formulation based on alpha-splines. By means of the proposed approach, non-integer values for the spline order can be employed in an appropriate mathematical framework, allowing its use as a real variable in any design procedure. Design examples demonstrate that smaller approximation errors than other approaches based on conventional windows can be obtained.

• 出版日期2016-5