Computationally efficient low roundoff noise second-order state-space structures

A new technique is introduced for synthesizing low roundoff noise second-order state-space structures. The technique yields structures which require the same number of multiplies as the canonical direct form structure. Thus
n
th-order realizations composed of these subfilters require only about 2
n
multiplies. The number of additions required is also low, ranging from 2
n
to 2.5
n
. The synthesis of these structures consists of simple design equations and a simple procedure. A numerical example illustrating the design process is provided.