Discrete time window functions with arbitrarily low sidelobe level

Abstract The most common approach to establish a set of window coefficients, representing the discrete time window (data window), is to select a suitable one from the well-known collections of continuous time window functions by simply sampling techniques. The simplicity of this approach has its price in certain complications which become more and more obvious as the number N of window coefficients decreases to small values ( N about 20 or less). It can be shown, that the DFT-even sampling technique as proposed by Harris [1] is not the most suitable one. Since both the aliasing effects as well as the relative position of the sampling raster gain influence on the resulting window magnitude spectrum in such a way that they must be checked individually, it turns out to be better to change the whole design strategy. The design of discrete windows is changed into an optimization problem within the set of all potential window coefficient vectors of given dimension. We apply the optimization criterion of Landau and Pollak [9]. One important advantage of this approach is that the optimization of the window coefficients is reduced to the proper selection of one single parameter which in a monotonic manner controls the trade-off between the two relevant window features mainlobe width and sidelobe level.