Consider the α-filter of Problem. Parts of this problem are repeated from Problem. Use those results if available.
(a) Write the state equations of the filter, with the state variable equal to the output y[n].
(b) Use the results of Part (a) to find the filter transfer function.
(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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