A frequency spectrum analyzing apparatus for performing a frequency spectrum analysis with respect to a detected value of an operating parameter of an internal combustion engine in synchronism with rotation of said engine, said frequency spectrum analyzing apparatus comprising: sampling means for sampling the operating parameter at predetermined time intervals, and converting a sampled value (VKNK(k)) to a digital value; sine-wave Fourier coefficient contribution calculating means for calculating, for each sampled value (VKNK(k)) of a predetermined number of sampled values (VKNK(k)) sampled within a sampling period synchronized with the rotation of the engine, the sine-wave Fourier coefficient contributions (DMFTS(j,k)) of this each sampled value (VKNK(k)) to the actual sine-wave Fourier coefficients corresponding to a plurality of frequency components contained in the detected value; cosine-wave Fourier coefficient contribution calculating means for calculating, for each sampled value (VKN K(k)) of the predetermined number of sampled values (VKNK(k)) sampled within the sampling period, the cosine-wave Fourier coefficient contributions (DMFTC(j,k))) of this each sampled value (VKNK(k)) to the actual cosine-wave Fourier coefficients corresponding to the plurality of frequency components; frequency Fourier coefficient calculating means for calculating (S5, S6), for each sampling period, frequency Fourier coefficients (STFT(j,i)) corresponding to the plurality of frequency components in synchronism with the rotation of said engine, on the basis of the sine-wave Fourier coefficient contributions (DMFTS(j,k)) and the cosine-wave Fourier coefficient contributions (DMFTC(j,k)), wherein said frequency Fourier coefficient calculating means is adapted to calculating the frequency Fourier coefficients (STFT(j,i)) on the basis of the sum of the sine-wave Fourier coefficient contributions (DMFTS(j,k)) over the predetermined number of sampled values (VKNK(k)) and of the sum of the cosine-wave Fourier coefficient contributions (DMFTC(j,k)) over the predetermined number of sampled values (VKNK(k)), the sums being calculated for a current sampling period, when a rotational speed of said engine is lower than a set threshold value (NETH), and wherein said frequency coefficient calculating means is adapted to calculating the frequency Fourier coefficients (STFT(j,i)) by replacing a part of the sum of the sine-wave Fourier coefficient contributions (DMFTS(j,k)), and a part of the sum of the cosine-wave Fourier coefficient contributions (DMFTC(j,k)) respectively, with corresponding values calculated for a preceding sampling period, when a rotational speed of said engine is higher than or equal to a set threshold value(NETH). sampling means for sampling the operating parameter at predetermined time intervals, and converting a sampled value (VKNK(k)) to a digital value; sine-wave Fourier coefficient contribution calculating means for calculating, for each sampled value (VKNK(k)) of a predetermined number of sampled values (VKNK(k)) sampled within a sampling period synchronized with the rotation of the engine, the sine-wave Fourier coefficient contributions (DMFTS(j,k)) of this each sampled value (VKNK(k)) to the actual sine-wave Fourier coefficients corresponding to a plurality of frequency components contained in the detected value; cosine-wave Fourier coefficient contribution calculating means for calculating, for each sampled value (VKN K(k)) of the predetermined number of sampled values (VKNK(k)) sampled within the sampling period, the cosine-wave Fourier coefficient contributions (DMFTC(j,k))) of this each sampled value (VKNK(k)) to the actual cosine-wave Fourier coefficients corresponding to the plurality of frequency components; frequency Fourier coefficient calculating means for calculating (S5, S6), for each sampling period, frequency Fourier coefficients (STFT(j,i)) corresponding to the plurality of frequency components in synchronism with the rotation of said engine, on the basis of the sine-wave Fourier coefficient contributions (DMFTS(j,k)) and the cosine-wave Fourier coefficient contributions (DMFTC(j,k)), wherein said frequency Fourier coefficient calculating means is adapted to calculating the frequency Fourier coefficients (STFT(j,i)) on the basis of the sum of the sine-wave Fourier coefficient contributions (DMFTS(j,k)) over the predetermined number of sampled values (VKNK(k)) and of the sum of the cosine-wave Fourier coefficient contributions (DMFTC(j,k)) over the predetermined number of sampled values (VKNK(k)), the sums being calculated for a current sampling period, when a rotational speed of said engine is lower than a set threshold value (NETH), and wherein said frequency coefficient calculating means is adapted to calculating the frequency Fourier coefficients (STFT(j,i)) by replacing a part of the sum of the sine-wave Fourier coefficient contributions (DMFTS(j,k)), and a part of the sum of the cosine-wave Fourier coefficient contributions (DMFTC(j,k)) respectively, with corresponding values calculated for a preceding sampling period, when a rotational speed of said engine is higher than or equal to a set threshold value(NETH).