An analysis is made of a system utilizing modulation and synchronous detection. The signal after modulation is expressed both as a Taylor expansion and as a Fourier series. The evaluation of the coefficients and subsequent comparison show that the first derivative of the signal can be expressed asf′(x)=A−1[H1−3H3+5H5−7H7+…+(−1)n−1(2n−1)H2n−1+…),whereAis the amplitude of the cosine modulation andH1,H3, etc., are the amplitudes of the odd harmonics of the modulated signal.