(a) Find a state model for the α-filter described by the equation
y[n + 1] – (1 – α)y[n] = αx[n + 1],
where x[n] is the input signal. Hint: Draw a simulation diagram first.
(b) Verify the results of Part (a) by (i) finding the transfer function from the describing equation and (ii) finding the transfer function from the state equations.
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