Linearity and time-invariance forcontinuous-time systems
Consider the followingsystems; where x(t) is the input and y(t) is the output:
1. y(t) = t^2x(t-1)
2. y(t) = sin(x(t))
3. y(t) = {x(t), t>= 0: 0, t<0}
4. y(t) = x(t)u(t) = {x(t), t>=0 : 0, t<0}
5. y(t) = { x(t),x(t)>=0 : 0, x(t)<0}
For each system,
a. Determine analytically whether or not it is linear and whether or not it is time-invariant.
b. Using test signals of your choice, such as the squarepulse x(t)=u(t)-u(t-1), write a Matlab program to illustrate yourresults. For each system plot the input and outputsignals.
You may use subplot for eachinput/output pair.
Remarks:
To prove that a system islinear or time-invariant, the property must be demonstrated for all possible input/output pairsand all delays. On the other hand, to prove that a system is not linear or not time-variant,the property can be demonstrated with only one input/output pair or delay.