16.2 Causal Stable LW-Systenis 3813 system function W ( z ) for a causal, stable, discrete IXLsystem must lie within t,he rwi( circle of the z-pli3ne f The genctal statemeiits CRU IN>inndc more precise for svsteizis for which the transfer function i s rational Their sixigularities are siinplc or inultiple poles ilial cfelint tlie charact eristic fr ecluencies of the system We caii describe t l m e systems with pole-zcro diagrams functioii H (s) for caiisal and stable roritinuous left half of t lit s-plane 1x1 _.1 'PO illustrate this property w e m i s t recall the interilitl term ylzlT( ) of (be output, sigiial from Chapter 3 It describes the part of the output sigiial tltat is caused by the initial slate of the system The Laplace transform of the int,ernal tcrrri can be represented (set (7.92)) by pwti tioris with poles s, In the time-tlornein this coiresponds t i t the sum of the 1's characteris