A Single Matrix Representation for General Digital Filter Structures [Lecture Notes]

A matrix representation of a general single-input single-output (SISO) digital filter structure is addressed, proposing a single matrix that stores the complete description of the filter in a very compact and functional format. The proposed matrix contains the structural information corresponding to the block diagram (BD) connections and, at the same time, it can be seen as a valid computational algorithm to implement the filter in the time domain. With this matrix, the gap between the signal flow graph (SFG) and a bit-true implementation of the filter can be considerably reduced. Finally, simple methods to derive the matrix representation from/onto the block diagram and the state-space (SS) mapping are also described and illustrated with some examples.