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How do I implement an Infinite Impulse Response (IIR) filter using Finite State Machine(FSM)? The problem is FSM has finite memory, but an IIR filter has infinite outputs. The closest match is this paper . Unfortunately I do not have access to the paper.

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Use feedback from output to input to perpetuate the output of the state machine. You don't need an infinite number of states to produce an infinitely long output sequence. For example, a state machine with a single memory element and feedback can be used to implement a first order IIR filter. An example of such a system has the recursion relationship y[n] = 0.5y[n-1] + x[n] where y is the output x is the input and 0.5y[n-1] is the past output scaled, fedback and summed with the input x[n].

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