Weight functions based on the convolutions of atomic functions

In the report new weight functions with low side-lobe level, based on convolutions of atomic functions are presented. There are effective algorithms for their computation. To increase coherent gain the window is truncated with an additional one. This approach allows us to obtain windows with good properties. The degree of cut of the function determines the relation between side-lobes and coherent gain. Usually the best windows are obtained with the cut near the effective support of function.