Reference no: EM13534538

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.