New windows for tunable length fir filter design

We discuss a new class of window functions based on the inverse of the product of two Gamma functions. These windows depend on two parameters and have performance similar to the Kaiser windows. By a proper selection of the two parameters we obtain windows that have the additional interesting property that smaller parts of the whole window are indeed efficient windows in the same class. If such a window is used to design a FIR filter, subsets of coefficients of the whole filter are efficient FIR filters of lower order. The possibility to tune the length of a filter to adapt to changing ressources such as processing time or power is a desirable property in highly integrated mobile devices.