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Homework Statement
Consider the continuoustime processing system in figure 1, which has two inputs and one output. The linear subsystem H is characterised by the impulse response h(t) = e −2t , where t denotes time.
Block diagram is the product of x1(t) and x2(t) going through a block step of h(t) (exp2t)
Give a mathematical proof that this is a nonlinear system.
Question attached in picture.
Homework Equations
α1y1(t) + α2y2(t) = H {α1x1(t) + α2x2(t)} , condition for linear stability
where x1(t) and x2(t) are two input signals and y1(t) and y2(t) are the corresponding output signals for system H
The Attempt at a Solution
Would my equations become
y1(t) = x1(t)e(2t)
y2(t) = x2(t)e(2t)
then calculating one way
y(t) = α1x1(t)e(2t) + α2x2(t)e(2t)
then the other
y(t) = e(2t)[α1x1(t) + α2x2(t)] = α1x1(t)e(2t) + α2x2(t)e(2t)
But that would suggest linearity... Is there something I'm missing?
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