TABLE OF CONTENTS The theory of LTI systems is a mature theory that has been well developed. [4] For our pr cis, only those results we shall use will be discussed. To begin, a system depicted in Fig. 5.1 is simply something for which there is a rule by which input waveforms x( t) are mapped into output waveforms y( t).
A system is time invariant (TI) if the rule does not vary with time. A system is linear if, for any constants C 1 and C 2 and for any inputs x 1( t) and x 2( t), the input x( t) = C 1 x 1( t) + C 2 x 2( t) results in the output y( t) = C 1 y 1( t) + C 2 y 2( t) in which y 1( t) is the output resulting from the input x 1( t) and y 2( t) is the output resulting from the input x 2( t). This is called generalized superposition so that a linear system is one that satisfies generalized superposition. A system that is both linear and TI is referred to as an LTI system.
We shall only be interested in LTI systems that are bounded-input bounded-output (BIBO) stable. A system...
