# Translations:Delay in general/33/en

The inverse of a minimum-delay filter *A*(*Z*) is , which also is a minimum-delay filter. An important type of stable causal IIR (infinite-impulse-response) filter is the recursive filter, which has its transfer function given by the rational function with the provision that the denominator polynomial *A*(*Z*) is a minimum-delay polynomial (i.e., all the roots of the polynomial lie outside of the unit circle). This provision ensures that the recursive filter is stable (Treitel and Robinson, 1964^{[1]}). The locations of the zeros of the numerator polynomial *B*(*Z*) do not need to be specified for the recursive filter to be stable. However, if it is further specified that the numerator polynomial *B*(*Z*) is a minimum-delay polynomial, the recursive filter is a minimum-delay filter.

- ↑ Treitel, S., and E. A. Robinson, 1964, The stability of digital filters: IEEE Transactions on Geoscience Electronics,
**GE-2**, 6–18.