Canonical pipelining of lattice filters

A variant of the lattice form is proposed in which delay elements are placed on both the upper (feedforward) path and the lower (feedback) path alternately. Although this new form preserves the fundamental characteristics of the usual lattice form having all the delay elements on the lower (feedback) path, it has some practical advantages. First, it represents a completely pipelined systolic-type array processor. The pipelining is canonical in the sense that no extra delay is introduced, Second, the finite word length performance is shown to be superior to that of the usual lattice form when it is used to implement digital filters of general transfer functions. The theoretical reasoning for this improvement is discussed based on the state-space representation. It is also shown that the new lattice form is topologically equivalent to the wave digital filter composed of the unit elements, which gives the physical ground of this new form.