Complex cascade programming and associated computional errors

A technique is described which enables a pulsed transfer function with complex poles and zeros to be cascade-programmed. Owing to the finite wordlength of the computer, computational errors arise when the realisation is used to process information. These can be represented in the steady state by a set of spurious error sequences additively contaminating the output of an ideal realisation. The shaping filters relating these error sequences to simple roundoff errors are derived.