Question: A discrete-time system has an input x(n) and output y(n). For n 0 it is described by the linear, constant-coefficient difference equation: y(n)-2.501y(n 1)

A discrete-time system has an input x(n) and output y(n). For n

A discrete-time system has an input x(n) and output y(n). For n 0 it is described by the linear, constant-coefficient difference equation: y(n)-2.501y(n 1) +2.1157 y(n 2)-0.5917 y(n 3)= 0.024x(n 1)+0.0054x(n 2) Find the transfer function H(z) of the system. Assume zero initial conditions. Given that the input to the system is a discrete-time sinusoid commencing at n = 0, i.e. x(n) = cos(n)u(n), find the steady-state response of the system for the six special frequencies: 2, = 0, 7, 3, 5, 7, 7.

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