2.6 A fundamental property of linear time-invariant systems is that whenever the input of the system is a sinusoid of a certain frequency the output will also be a sinusoid of the same frequency but...

Extracted text: 2.6 A fundamental property of linear time-invariant systems is that whenever the input of the system is a sinusoid of a certain frequency the output will also be a sinusoid of the same frequency but 160 CHAPTER 2 CONTINUOUS-TIME SYSTEMS with an amplitude and phase determined by the system. For the following systems let the input be x (t) = cos(t), -0 < o∞,="" find="" the="" output="" y(t)="" and="" determine="" if="" the="" system="" is="" lti:="" (a)="" -y(1)="[x(1)|²," (c)="" y(t)="x(1)u(t)," (d)="" y(1)=";" f,-2×(t)dt.="" (b)="" y(t)="0.5[x(t)+x(t=" 1)],="" answers:="" (a)="" y(t)="0.5(1+cos(2t));" (c)="" system="" is="" not="">