A Recursive Demodulator for Real-Time Measurement of Multiple Sinusoids

Shijie Sun, Lijun Xu, Zhang Cao, Jiangtao Sun, Wuqiang Yang

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A fast demodulator for real-time measurement of the amplitudes and phases of multiple sinusoids is highly desired in many applications. When the sampling frequency is fixed, the number of samples needed for demodulation determines the time consumption and hence the demodulation speed. In this paper, a quadrature demodulation method is first presented, which requires that the samples cover exactly integer periods of the multi-frequency signal. Second, a new recursive demodulation method is proposed, which can not only overcome the limitation of the quadrature method but also provide greater flexibility between accuracy and speed, i.e., either to obtain a higher speed at an expense of a lower accuracy, or vice versa. The proposed method can work with a sample series of any length as long as more than twice the number of sinusoids and generate demodulation results for all sinusoids simultaneously. Third, a resource-saving and fast implementation of the recursive demodulator was proposed and constructed on a digital signal processor/field-programmable gate array, which enables in situ and online application of the recursive demodulator. Experiments were carried out to investigate the performance of the proposed demodulator, including relative error, standard deviation, and their variations with the number of samples involved in the demodulation and compared with other conventional methods.
Original languageEnglish
Pages (from-to)6281-6289
Number of pages9
JournalIEEE Sensors Journal
Issue number15
Early online date6 Jun 2018
Publication statusPublished - 1 Aug 2018


  • Recursive demodulator
  • demodulation speed
  • quadrature method


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