A bearing including an inner ring, an outer ring, and rolling bodies positioned between said inner and outer rings, one of said rings being rotary and the other not, said bearing characterized in that it comprises: - a first processing module which is fixed on one of the inner or outer rings (11, 12) and includes a radiofrequency transmitter, and a set of at least one sensor suitable for performing successive measurements of at least one parameter representative of the vibrations within the bearing; and - a further processing module which is integrated into the bearing and located in a position other than that of the first processing module; and in that - said first processing module is configured for applying a frequency transform for determining a frequency representation of the signal corresponding to the successive measurements, and for obtaining a set of at least one element representative of said frequency representation as a function of that frequency representation, wherein the radiofrequency transmitter is configured to send to the further processing module the digital data of the obtained set of at least one element representative of said frequency representation as a function of that frequency representation; and wherein said further processing module is configured to compare at least one representative element of said set with a corresponding reference element and identify a malfunction as a function of that comparison; and wherein the first processing module is configured such that the time separating two successive time samples considered for the frequency transform depends on the relative speed of rotation between the two inner and outer rings; and wherein said speed is determined from measures issued by a sensor of the set of at least one sensor that is included in said first processing module fixed on one of the inner or outer rings (11, 12) of_the bearing. - a first processing module which is fixed on one of the inner or outer rings (11, 12) and includes a radiofrequency transmitter, and a set of at least one sensor suitable for performing successive measurements of at least one parameter representative of the vibrations within the bearing; and - a further processing module which is integrated into the bearing and located in a position other than that of the first processing module; and in that - said first processing module is configured for applying a frequency transform for determining a frequency representation of the signal corresponding to the successive measurements, and for obtaining a set of at least one element representative of said frequency representation as a function of that frequency representation, wherein the radiofrequency transmitter is configured to send to the further processing module the digital data of the obtained set of at least one element representative of said frequency representation as a function of that frequency representation; and wherein said further processing module is configured to compare at least one representative element of said set with a corresponding reference element and identify a malfunction as a function of that comparison; and wherein the first processing module is configured such that the time separating two successive time samples considered for the frequency transform depends on the relative speed of rotation between the two inner and outer rings; and wherein said speed is determined from measures issued by a sensor of the set of at least one sensor that is included in said first processing module fixed on one of the inner or outer rings (11, 12) of_the bearing. the radiofrequency transmitter is configured to send to the further processing module the digital data of the obtained set of at least one element representative of said frequency representation as a function of that frequency representation; and wherein said further processing module is configured to compare at least one representative element of said set with a corresponding reference element and identify a malfunction as a function of that comparison; and wherein the first processing module is configured such that the time separating two successive time samples considered for the frequency transform depends on the relative speed of rotation between the two inner and outer rings; and wherein said speed is determined from measures issued by a sensor of the set of at least one sensor that is included in said first processing module fixed on one of the inner or outer rings (11, 12) of_the bearing.