In this chapter we introduced a number of general properties

In this chapter, we introduced a number of general properties of systems. In particular,
a system may or may not be
(1) Memoryless
(2) Time invariant
(3) Linear
(4) Causal
(5) Stable
Determine which of these properties hold and which do not hold for each of the
following continuous-time systems. Justify your answers. In each example, y(t) denotes
the system output and x(t) is the system input.

(b) y(t) = [cos(3t)]x(t)

(f) y(t) = x(t/3)

Solution

b)

y(t)=[cos(3t)]x(t)

its memoryless system, since its not holding any past or future output values

y(t+T)=[cos(3t+3T)]x(t+T)

y(t,T)=[cos(3t)]x(t+T)

y(t+T),y(t,T) both are not equal so its time variant system

its causal system since, the system depends only present input

its stable system, since its gives stable output for Bounded inputs.

f)y(t)=x(t/3)

(i)its Memory or dynamic system, since the output of the system depends past input

for example t=3, y(3)=x(3/3)=x(1);

(ii)its time variant system

y(t+T)=x((t+T)/3)

y(t,T)=x((t+T)/3)

y(t+T)=y(t,T) so time varaiant system

(iii)its linear system

(iV)its casal sytem since the output of the system depends past input

(v)its stable sytem,because its give stable output for bounded input