Harmonic Analysis in Systems Using Phase Sensitive Detectors

Abstract

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 as $${\mathrm{f\prime (x)=A}}^{\text{−1}}{\mathrm{[H}}_1{\text{−3H}}_3{\text{+5H}}_5{\text{−7H}}_7{\text{+…+(−1)}}^{\text{n−1}}{\text{(2n−1)H}}_{\text{2n−1}}\mathrm{+\dots )}$$ , where A is the amplitude of the cosine modulation and H₁, H₃, etc., are the amplitudes of the odd harmonics of the modulated signal.