The article presents an example of the use of functional series for the analysis of nonlinear systems for discrete time signals. The homogeneous operator is defined and it is decomposed into three component operators: the multiplying operator, the convolution operator and the alignment operator. An important case from a practical point of view is considered – a cascade connection of two polynomial systems. A new, binary algorithm for determining the sequence of complex kernels of cascade from two sequences of kernels of component systems is presented. Due to its simplicity, it can be used during iterative processes in the analysis of nonlinear systems (e.g. feedback systems).