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Design of window function using spline functions

In our previous paper, it was shown that the rectangular, triangular and Parzen windows can be generalized as a B-spline function according to its order. That series of window functions has a merit in that a fast fall-off of the sidelobe is realized by increasing the parameter, i.e., the order, while it has a demerit in that the bandwidth of the mainlobe is increased. This paper aims at the improvement of this point, and proposes a design method whereby the window function is represented by a linear combination of B-spline functions. As an example of the window function obtained by the proposed method, a window function is presented which has the same mainlobe bandwidth and highest sidelobe level as Hanning or Blackman window, and still has a faster fall-off. Almost the same quality of approximation as the Hanning or Blackman window is also demonstrated.