Poles, zeros, and sheaf cohomology Original Research Article

The Fundamental Pole–Zero Exact Sequence for a transfer function matrix, first enunciated in 1989, supplies a structural meaning to the hope that “the number of zeros of a transfer function is the same as the number of poles”. This principle requires the inclusion of generic zeros counted using Wedderburn–Forney spaces which measure the kernel and cokernel of the transfer function. In this brief note we identify the Wedderburn–Forney space as a cohomology group and give a new approach to the Fundamental Pole–Zero Exact Sequence in terms of exact sequences of sheaf cohomology groups.