An apparatus for detecting a tire having a decreased air pressure comprising: a wheel rotation speed information detection means for detecting rotation speed information of the respective wheels (FL, FR, RL, RR) of a vehicle; a frequency characteristic estimate means for estimating, based on the wheel rotation speed information obtained by the wheel rotation speed information detection means, a frequency characteristic of the wheel rotation speed information; and a decreased air pressure determination means for determining, based on the estimated frequency characteristic, a tire having a decreased air pressure wherein the frequency characteristic estimate means includes, to a time-series signal including the wheel rotation speed information: a parameter estimate means for performing a first step of time-series estimating a third order or more linear model parameter; a pseudo input data generating means for performing a second step of generating pseudo input data; an output data estimate means for performing a third step of estimating, based on the linear model parameter estimated in the first step and the pseudo input data generated in the second step, output data to a linear model; a parameter identification means for performing a fourth step of identifying, based on the pseudo input data and the estimated output, a linear model parameter for which the order is reduced to a second order; and a resonance frequency estimate means for performing a fifth step of estimating, based on the identified parameter for which the order is reduced to the second order, a resonance frequency of a tire torsional direction,and wherein the decreased air pressure determination means is so configured as to determine a tire having a decreased air pressure based on the estimated resonance frequency of the tire torsional direction. a wheel rotation speed information detection means for detecting rotation speed information of the respective wheels (FL, FR, RL, RR) of a vehicle; a frequency characteristic estimate means for estimating, based on the wheel rotation speed information obtained by the wheel rotation speed information detection means, a frequency characteristic of the wheel rotation speed information; and a decreased air pressure determination means for determining, based on the estimated frequency characteristic, a tire having a decreased air pressure wherein the frequency characteristic estimate means includes, to a time-series signal including the wheel rotation speed information: a parameter estimate means for performing a first step of time-series estimating a third order or more linear model parameter; a pseudo input data generating means for performing a second step of generating pseudo input data; an output data estimate means for performing a third step of estimating, based on the linear model parameter estimated in the first step and the pseudo input data generated in the second step, output data to a linear model; a parameter identification means for performing a fourth step of identifying, based on the pseudo input data and the estimated output, a linear model parameter for which the order is reduced to a second order; and a resonance frequency estimate means for performing a fifth step of estimating, based on the identified parameter for which the order is reduced to the second order, a resonance frequency of a tire torsional direction,and wherein the decreased air pressure determination means is so configured as to determine a tire having a decreased air pressure based on the estimated resonance frequency of the tire torsional direction. a parameter estimate means for performing a first step of time-series estimating a third order or more linear model parameter; a pseudo input data generating means for performing a second step of generating pseudo input data; an output data estimate means for performing a third step of estimating, based on the linear model parameter estimated in the first step and the pseudo input data generated in the second step, output data to a linear model; a parameter identification means for performing a fourth step of identifying, based on the pseudo input data and the estimated output, a linear model parameter for which the order is reduced to a second order; and a resonance frequency estimate means for performing a fifth step of estimating, based on the identified parameter for which the order is reduced to the second order, a resonance frequency of a tire torsional direction,and wherein the decreased air pressure determination means is so configured as to determine a tire having a decreased air pressure based on the estimated resonance frequency of the tire torsional direction.