Chap1_properties_sol

Chap1_properties_sol - 1. a) dy + 6y( t ) = 4 x ( t ) dt...

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1. a) dy dt yt xt += 64 () This is an ordinary differential equation with constant coefficients, therefore, it is linear and time- invariant. It contains memory and it is causal. b) dy dt ty t x t 42 This is an ordinary differential equation. The coefficients of 4t and 2 do not depend on y or x, so the system is linear. However, the coefficient 4t is not constant, so it is time-varying. The system is also causal and has memory c) This is a difference equation with constant coefficients; therefore, it is linear and time-invariant. It is noncausal since the output depends on future values of x. Specifically, let x[n] = u[n], then y[-1] = 1. d) y(t) = sin(x(t)) check linearity: 11 () s in ( () ) = 22 ) = Solution to an input of ax t ax t 2 2 + is s ( ) + . This is not equal to ay t ay t + . As a counter example, consider 1 and 2 2 / , aa 12 1 == the system is causal since the output does not depend on future values of time, and it is memoryless the system is time-invariant e) dy dt yt x t 2
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Chap1_properties_sol - 1. a) dy + 6y( t ) = 4 x ( t ) dt...

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