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In signal processing, a recursive filter is a type of filter which re-uses one or more of its outputs as an input. This feedback typically results in an unending impulse response ], characterised by either exponentially growing, decaying, or sinusoidal signal output components.
However, a recursive filter does not always have an infinite impulse response. Some implementations of moving average filter are recursive filters but with a finite impulse response.
Non-recursive Filter Example:y = 0.5x + 0.5x.
Recursive Filter Example:y = 0.5y + 0.5x.
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