# Translations:Inverse filters/37/en

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Suppose that we then build a causal FIR filter with the five-length memory function (0.03125, –0.0625, 0.125, –0.25, 0.5). Because this filter is an FIR filter, it necessarily is stable. If we let the time series be the input to this filter, the output at time index *n* = 8 will be an approximation to the desired . In other words, to approximate the desired output , we have introduced a time delay of 8 – 3 = 5 time units, thereby obtaining a causal FIR filter with a five-length memory function. By increasing this time delay, we can obtain causal FIR filters that yield better approximations. A perfect approximation is reached only by introducing an infinite time delay (Treitel and Robinson, 1969^{[1]}).

- ↑ Treitel, S., and E. A. Robinson, 1969, Optimum digital filters for signal to noise ratio enhancement: Geophysical Prospecting,
**17**, 248–293.