Signals and Systems 2nd edition Oppenheim chapter 1 problem 27 a) - g) In this c

Question

Signals and Systems 2nd edition Oppenheim chapter 1 problem 27 a) - g)

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.

a) y(t) = x(t-2) + x(2-t)

b) y(t) = cos(3*t)*x(t)

c) y(t) = integral(x(t)*dt,t,-infinity,2*t)

d) y(t) = ( 0 t< 0 , x(t) + x(t-2) t>=0 )

e) y(t) = ( 0 x(t)< 0 , x(t) + x(t-2) x(t)>=0 )

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

g) y(t) = d/dt*(x(t))

Explanation / Answer

1).A system is said to be memoryless if the output at any time depends on only the input at that same time. 2).A system is called time-invariant if a time shift (delay or advance) in the input signal causes the same time shift in the output signal. 3).for a system T(x1)=y1 if T(x1+x2)=y1+y2 then system is linear 4).the output y ( t ) does not depend on the future values of the input x(t),then the system is causal. 5).a system is said stable if for any input x bounded with any value the output is also bounded take hint from these definitions hope this helps

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