# Translations:Minimum-phase spectrum/23/en

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Let us restrict ourselves to real weighting coefficients, and let us consider only causal digital filters, for which the output can never precede the input in time. Then we see that the pair of causal FIR filters *F*(*Z*) and *G*(*Z*) represents a set of digital causal filters, each of which has the same amplitude spectrum. This set of causal filters is exhaustive in the sense that the two real weighting coefficients 1 and 0.5 can occur only in the sequence (1, 0.5) or in the sequence (0.5, 1). Now we can say that the filter *F*(*Z*) has the *minimum-phase spectrum* of the filter set {*F*(*Z*), *G*(*Z*)}.