1.2 systcllx -~ 111s t heorv clocs not ciiconipass the implerrretit at i w ot a relatiorirhips Clrat, the system iinposcs bet wtwi its sigonrrits hi,with nals Svstems lheory I Pscrit s a powrrfid xnathcwiaticaJ tool for tlw stud\ and mentation details h l p s to inniritaiii bccttusc ontitting the i c~ebigrror s t b c ~ r ythc focus is 011 the formal an overview of the ovrrall systcixi In s ny sprcialisation for specific applinat me of the irit erc or111 ions ‘I’hi.; allrrvvs systeiris theory a, unilorm rvprescJrital ioir of procc on tlonieiiis (P g., physics, enginecrinp,, econoinics, biology) arid iisciyliriarv view The high t l c y g w ot abstraction b gs the advcirrtages of learriiiig ccwioniy m d clar its 1,cai ning econorriy c~isiir:,k n n u l d ~ din griirial form Clarity rcsults bcmnsc separating the ctrt>iilproblems froin the gciieral relat,iorisliips i s clcvatcd to n priiiriplc However this i s countcirtvl by t h c drawback ot a cer l a i r ; ~ r r i o u n t of unclcariiess tliat enciurihri~sinitial leavriirig iir systeiiis tliror y ear, Iln important sihfirld of ms thcor! is t Ire l i ~ o r vof liiicar, time-invariarit systems ‘I his repicsmts tl assical core ciomain of s y s k r m t Iicw J- nncl i h -cvell develtq~xl,elrgatit arid clear This throry also prows suitable for describiiig I ~ I tcms Iliat caii bc Iiiitw small signal aiiiplitiitlcs bysi eins theory tiiiic-in\iariarrt syst froin tlie practical pirjt)l(ws ol electrical rnghwring over i~iorcthaii a t c Important a p p l i c a h n dolX*iLiri\ h r thr thcory of liiieai, time-invaria cleclxicitl erigirr irig totlav inc hide Aiinlysis a i d dcisign of clcctrical circuits e Digital sigml processing Clorrrmuriiw t ion? To tlefiire thr tcrm liucazfty, kit us considcr the systcni iri Figiirc 1.9 Ir respoiitl.; to an iriput signal r t ( t ) with tlic output signal $11( t )ant1 t o the input signal cZ(1) -