A design method of window functions by spline approximation

Abstract

AbstractIn a previous paper, the authors proposed a design method for representing the window function by the C‐spline function, which is a linear combination of the B‐spline functions. By using that design method, a window function is obtained which has the same mainlobe bandwidth and the highest sidelobe level as the Hanning window or Blackman window, but a faster sidelobe fall‐off. However, the design method for the new window function is not practical due to the fact that the description of the design specification is premature and the optimal dimension is not specified.This paper aims at the realization of a practical design method by improving those points. A design method is proposed in which the specification for the high‐frequency range is given in terms of the sidelobe fall‐off, and the specification for the low‐frequency range is given in terms of the desired frequency characteristics in the logarithmic scale, together with the tolerable approximation error, represented by the mean‐square error.The optimal dimension is determined, in the iterative approximation increasing the dimension to reduce the error in regard to the desired frequency characteristics, as the minimum dimension that reduces the error to the tolerable value. The usefulness of the proposed design method is demonstrated by a design example for the window function, which has a better characteristic than those of Kaiser‐Bessel, Gauss and Hanning windows.