Review of Scientific Instruments · 1962 · 28 citations · 1 references
EngineeringElectrical EngineeringAnalog ElectronicsSensorsTime Series AnalysisDigital Signal ProcessingHarmonic AnalysisModulationSignal Detection TheorySignal ProcessingTime-frequency AnalysisFourier Series AnalysisHarmonic Spectrum AnalysisHarmonicsModulation AnalysisPhase-sensitive DetectionSignal Detection Circuits
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 f′(x)=A−1[H1−3H3+5H5−7H7+…+(−1)n−1(2n−1)H2n−1+…),where A is the amplitude of the cosine modulation and H1, H3, etc., are the amplitudes of the odd harmonics of the modulated signal.
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