Nonrecursive filter
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In mathematics, a nonrecursive filter only uses input values like x[n − 1], unlike recursive filter where it uses previous output values like y[n − 1].
In signal processing, non-recursive digital filters are often known as Finite Impulse Response (FIR) filters, as a non-recursive digital filter has a finite number of coefficients in the impulse response h[n].[1]
Examples:
- Non-recursive filter: y[n] = 0.5x[n − 1] + 0.5x[n]
- Recursive filter: y[n] = 0.5y[n − 1] + 0.5x[n]
An important property of non-recursive filters is, that they will always be stable. This is not always the case for recursive filters.
References
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- ^ Page Module:Citation/CS1/styles.css has no content.Helms, H (September 1, 1968). "Nonrecursive digital filters: Design methods for achieving specifications on frequency response". IEEE Transactions on Audio and Electroacoustics. 16 (3): 336–342. doi:10.1109/TAU.1968.1161999.
