An apparatus for analyzing an element rotating at a rotational speed based on a vibration signal originating from the rotating element, comprising: analysis function means for forming a plurality of analysis functions, the analysis function means being configured to form each analysis function based on an analysis frequency, based on the vibration signal or based on a measured or estimated rotational speed and based on a predetermined order factor, the predetermined order factor differing for each analysis function; correlation means for calculating a correlation function, the correlation means being configured to calculate a correlation result from the vibration signal and each analysis function, each correlation result being associated to the order factor which the analysis function, with which the correlation result was calculated, is based on, and the correlation results representing the correlation function; and examining means for examining the correlation function or for examining information derived from the correlation function so as to make a statement on a state of the rotating element, characterized in that the analysis function means is configured to calculate the analysis functions h (t, τ, s) based on the following equation: h t τ s = exp j 2 πsft + jsr t + τ, t being a time variable, τ being a time shift, s representing the order factors for each analysis function, f being the analysis frequency and r(t+τ) being a phase term dependent on the vibration signal or the rotational speed, or in that the correlation means is configured to calculate (50, 52) a preliminary correlation function using a preliminary time shift between the vibration signal and the plurality of analysis functions, establish a correction order factor of a local or global maximum of the preliminary correlation function, wherein the analysis function means is configured to calculate a plurality of correction analysis functions which are based on the same correction order factor and which comprise a different time shift, wherein the correlation means is configured to calculate a correction correlation function from the vibration signal and the plurality of correction analysis functions and evaluate the correction correlation function in order to establish a maximum associated to a correction time shift, wherein the analysis function means is configured to calculate correction analysis functions using the correction time shift, and wherein the correlation means is configured to calculate the correlation function based on the correction analysis functions which are based on the correction time shift. analysis function means for forming a plurality of analysis functions, the analysis function means being configured to form each analysis function based on an analysis frequency, based on the vibration signal or based on a measured or estimated rotational speed and based on a predetermined order factor, the predetermined order factor differing for each analysis function; correlation means for calculating a correlation function, the correlation means being configured to calculate a correlation result from the vibration signal and each analysis function, each correlation result being associated to the order factor which the analysis function, with which the correlation result was calculated, is based on, and the correlation results representing the correlation function; and examining means for examining the correlation function or for examining information derived from the correlation function so as to make a statement on a state of the rotating element, characterized in that the analysis function means is configured to calculate the analysis functions h (t, τ, s) based on the following equation: h t τ s = exp j 2 πsft + jsr t + τ, t being a time variable, τ being a time shift, s representing the order factors for each analysis function, f being the analysis frequency and r(t+τ) being a phase term dependent on the vibration signal or the rotational speed, or in that the correlation means is configured to calculate (50, 52) a preliminary correlation function using a preliminary time shift between the vibration signal and the plurality of analysis functions, establish a correction order factor of a local or global maximum of the preliminary correlation function, wherein the analysis function means is configured to calculate a plurality of correction analysis functions which are based on the same correction order factor and which comprise a different time shift, wherein the correlation means is configured to calculate a correction correlation function from the vibration signal and the plurality of correction analysis functions and evaluate the correction correlation function in order to establish a maximum associated to a correction time shift, wherein the analysis function means is configured to calculate correction analysis functions using the correction time shift, and wherein the correlation means is configured to calculate the correlation function based on the correction analysis functions which are based on the correction time shift.