(a) Show that causality for a continuous-time linear system is equivalent to the
Chapter 1, Problem 1.44(choose chapter or problem)
(a) Show that causality for a continuous-time linear system is equivalent to the following statement: For any time to and any input x(t) such that x(t) = 0 fort < t0, the corresponding output y(t) must also be zero fort < t0 . The analogous statement can be made for a discrete-time linear system. (b) Find a nonlinear system that satisfies the foregoing condition but is not causal. (c) Find a nonlinear system that is causal but does not satisfy the condition. (d) Show that invertibility for a discrete-time linear system is equivalent to the following statement: The only input that produces y[n] = 0 for all n is x[n] = 0 for all n. The analogous statement is also true for a continuous-time linear system. (e) Find a nonlinear system that satisfies the condition of part (d) but is not invertible.
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