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 (VKNK(k), k = 1...ND) at predetermined time intervals, and converting the sampled value to a digital value; sine coefficient contribution calculating means and cosine coefficient contribution calculating means for calculating, for each sampled value (VKNK(k), k = 1...ND) of a predetermined number of sampled values, sine coefficient contributions (DMFTS(j, k)) and cosine coefficient contributions (DMFTC(j, k)) of this sampled value (VKNK(k)) to sine coefficients (SUMDS(j)) and cosine coefficients (SUMDC(j)) corresponding to a plurality of frequency components ((j+5)kHz, j=0...20) contained in the detected values (VKNK(k)); and frequency component amplitude calculating means for calculating frequency component amplitudes (STFT(j, i) = (SUMDS(j) 2 +SUMDC(j) 2) 1/2) corresponding to the plurality of frequencies ((j+5)kHz, j=0...20) iri synchronism with rotation of said engine, using the sine coefficient contributions (DMFTS(j, k)) and the cosine coefficient contributions (DMFTC(j, k)); characterized in that said frequency component amplitude calculating means includes offset component calculating means for calculating offset components (VCNT-SUMQS(j), VCNT·SUMQC(j)) contained in the sine coefficient contributions (DMFTS(j, k)) and the cosine coefficient contributions (DMFTC(j, k)), and calculates the frequency component amplitudes (STFT(j, i)) after removing the offset components (VCNT-SUMQS(j), VCNT-SUMQC(j)) from the sine coefficient contributions (DMFTS(j, k)) and the cosine coefficient contributions (DMFTC(j, k)). sampling means for sampling the operating parameter (VKNK(k), k = 1...ND) at predetermined time intervals, and converting the sampled value to a digital value; sine coefficient contribution calculating means and cosine coefficient contribution calculating means for calculating, for each sampled value (VKNK(k), k = 1...ND) of a predetermined number of sampled values, sine coefficient contributions (DMFTS(j, k)) and cosine coefficient contributions (DMFTC(j, k)) of this sampled value (VKNK(k)) to sine coefficients (SUMDS(j)) and cosine coefficients (SUMDC(j)) corresponding to a plurality of frequency components ((j+5)kHz, j=0...20) contained in the detected values (VKNK(k)); and frequency component amplitude calculating means for calculating frequency component amplitudes (STFT(j, i) = (SUMDS(j) 2 +SUMDC(j) 2) 1/2) corresponding to the plurality of frequencies ((j+5)kHz, j=0...20) iri synchronism with rotation of said engine, using the sine coefficient contributions (DMFTS(j, k)) and the cosine coefficient contributions (DMFTC(j, k)); characterized in that said frequency component amplitude calculating means includes offset component calculating means for calculating offset components (VCNT-SUMQS(j), VCNT·SUMQC(j)) contained in the sine coefficient contributions (DMFTS(j, k)) and the cosine coefficient contributions (DMFTC(j, k)), and calculates the frequency component amplitudes (STFT(j, i)) after removing the offset components (VCNT-SUMQS(j), VCNT-SUMQC(j)) from the sine coefficient contributions (DMFTS(j, k)) and the cosine coefficient contributions (DMFTC(j, k)).