A Recursive Demodulator for Real-Time Measurement of Multiple Sinusoids

Abstract

Abstract-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 firstly presented, which requires that the samples cover exactly integer periods of the multi-frequency signal. Secondly, 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. Thirdly, a resource-saving and fast implementation of the recursive demodulator was proposed and constructed on a DSP/FPGA, which enables in-situ and on-line 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 compare with other conventional methods.Index Terms-Recursive demodulator, Quadrature method, Demodulation speed, DSP/FPGA I. INTRODUCTION n the active measurement of various object parameters, an external excitation signal is applied on the target object through a sensor. By measuring the response signal that carries the information of the object's characteristic parameters, the parameters to be measured can be derived. Sinusoid is a kind of commonly used excitation signal. To quickly obtain the target parameters of the object under excitation of a series of given frequencies, multiple sinusoids of the given frequencies can be combined as an excitation signal so that the unknowns are measured simultaneously. Because the response sensor signal is also composed of multiple sinusoids with the same frequencies and the frequencies are pre-known, only the amplitudes and phases of the sinusoids need to be obtained. The active measurement is required in many industrial and biomedical applications, such as industrial process tomography [1]- [3], bio-impedance measurement [4]- [6], eddy current testing [7], [8] and built-in self-test [9], etc. Because the characteristic parameters of the target object are often rapidly changing, real-time and fast measurement of the amplitudes and phases of multiple sinusoids in the response sensor signal is highly desired in sensor data processing.The demodulation process can be implemented using an analog method [10], which consists of multiplexers and filters. However, the demodulation speed is restricted by the highorder low-pass filters. In recent years, digital demodulators have been widely used, including the synchronous sampling method [11], the DFT, FFT [12]- [14] and...

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