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If a system has transfer function $H(z) = 1 + z^{–1} + z^{–2}$, then for an input signal of the sequence = {1,2,3,1,4,-2, 4} calculate the output sequence of the system.

DO i put transfer function into z trandform?

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2 Answers 2

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You simply solve by computing it into a table.

Please note the Transfer Function in Z Transform with polynomials of $1$, $z^{-1}$ and $z^{-2}$ are no more than discrete time step delays of t=0, 1 and 2 from the original signal, which are all added into a single expression.

That is, the $z$ is an "add one step time" operator.

enter image description here

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Solving the problem with Octave/MATLAB code:

x = [1,2,3,1,4,-2,4]; B = [1,1,1]; % H(z) coefficients A = [1]; Output = filter(B,A,x)

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