Signals and Systems Fall 2003 Lecture #2 9 September 2003 Some examples of systems 2) System properties and examples a) Causality b) linearity c)Time invariance
Signals and Systems Fall 2003 Lecture #2 9 September 2003 1) Some examples of systems 2) System properties and examples a) Causality b) Linearity c) Time invariance
SYSTEM EXAMPLES CT System DT SyStem Ex #1 RlC circuit R L x(t) i(t) C y(t) R i(t)+ a+∥) (+)=C LC dt2+rc ay(t) 9(
SYSTEM EXAMPLES x ( t) CT System y ( t) x[n] D T System y[n] Ex. #1 RLC circuit
Ex.#2 Mechanical system K x(t)-applied force K -spring constant D -damping constant y(t)-displacement from rest y(t) Force Balance (t) 2 dt may(t)+d dt +Ky(t)=a(t) Observation: Very different physical systems may be modeled mathematically in very similar ways
Force Balance: Observation: Very different physical systems may be modeled mathematically in very similar ways. Ex. #2 Mechanical system
Ex. #3 Thermal system Cooling fin in Steady state Temperature y(t) rlt t distance along rod y(t)=Fin temperature as function of position x(t)= surrounding temperature along the fin
Ex. #3 Thermal system Cooling Fin in Steady State
Ex. #3(Continued) kla(t).(t) 9(10 0 dt Observations Independent variable can be something other than time. such as space Such systems may, more naturally, have boundary conditions rather than"initial conditions
Ex. #3 (Continued) Observations • Independent variable can be something other than time, such as space. • Such systems may, more naturally, have boundary conditions, rather than “initial” conditions