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(Solved): Consider a discrete-time system with input x[n] and output y[n], respectively. Let * denote the op ...
Consider a discrete-time system with input
x[n]and output
y[n], respectively. Let * denote the operator taking convolution. (a)
(20%)Show that this system is linear and time-invariant (LTI) if and only if
y[n]=x[n]^(**)h[n]. where and
h[n]stands for the impulse response of the system. (b)
(10%)Given
h_(1)[n],h_(2)[n],h_(3)[n], show that
(h_(1)[n]^(**)h_(2)[n])^(**)h_(3)[n]=h_(1)[n]^(**)(h_(2)[n]^(**)h_(3)[n]). (c)
(5%)Based on (a) and (b), show that the serial interconnection of two LTT systems is also LTI.
