Question

For each of the following systems, determine which of the above properties hold.

5. General properties of systems. A system may or may not be: (a) Memoryless (b) Time Invariant (c) Linear (d) Causal (e) Stable For each of the following systems, determine which of the above properties hold. (a) y(t)sin(2t)x(t) { 0, x(t)2t 3) t20 t <0 (b) y(t) = (c) yn3[n ] -n-5] x[n], 0, n 1 (d) yn 0 n= n2, n< -1

Answer 1

NOTE STATIC AND OYNAWECSYSTEN. A System is static if Present in pupt only but nat past or future input the present oufpeut deperds on In Generat System withguf memory ae called as static less system memory System having memory dynamie system called as are ytrtantn1)= fast futune Solun sinlet1.nt 1. -7 an present valies here the olp ofthe system ie ytt) depevds only of elr re fit) So the sysdemn is called memory less system Ceefficiernt uned NOTE Static and dynamic are independort af n system aelationship co fficient of mith here SiO (2+) IS HLe Sa the pTesent and tast value 9t depends System i's dynawic system ie 2t is nat an a memory kss SyStem.

Yeni= 37Ih-1) - minS. elynamic system), becaune of if olepends an past t/ P. Min yens n- t dynamie sysdem), becauneofit depevds paesent ntn) and festarne mint2) Velue of p

VARPANT AND INe IMVARLANT A SyStem is time invaniant if its input-o/p characle1stics oloesn't chonge with time vt y (d-to nit-to) f de layedd input 1/t-to) rodures de lory ed o/p y -to than a SYStem s saidl to be timeo Vaaiant NOTE n system delaf16nghip is efficieat When loe fumesion af time then system will be ime veriant Gime vasiqnt > dueto sintot nt22n 3) >0 mE ENYARLANT Teflested must be because delay prouided in yen TEME I NVARLANT Min) C 2NVARPANT n2-1

LENEAR Cinear System follows the the scuper positian Sufficient painciple Cow of scuperposition S necessany to parove Ci,earity of system J+ is a CombinctHon of TuJu Lows CLOW of Additiuidy LOw Of HOmog inity. Sin (2t) nt). akne-CineaE. wed Cafficiant Lineasity of system is in sysdem relatrion ship. independent of LINEAR L2NERR 3n (4-11-nIn-s) LeNCAR ninf21 n2-1

CAUSAL jf olp of a system rs independert of futene vesleye of enpeut then system iscaledcauso 9t i's also Known as practica Physicaly negirgable cyStem year PCausdH gt depevds cn present elponly enpef. Coefficsenrt of the jt is imdepemdent ofth e NOTE +70 2n(4-3) LCeusal at olepevdls on prresent aved past value of becaune causaf yeml RON CeuuSal futeire Velue ntz). if olapard's Seceuse

STABLE Stable sysHem olp shou ld finite for fioile c be bourded enput (91 yta STABLE Let bounded /p is de ie na= 1 SinC2t) olp is also boundad So System is Stable +20 C6-ナ)して +()ん STABLE firite it gires o/p isalso /et froide elp nth-s 31(h-1) yeni STABLE a absolule Summasle- becaue y tnl= Mintz) STABLE