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�������պ����ѧѧ�� 2007, Vol. 33 Issue (05) :580-584    DOI:
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�������պ����ѧ ������Ϣ����ѧԺ, ���� 100083
Phase estimation of sinusoid signal based on DFT and error analysis
Li Chunyu, Zhang Xiaolin, Zhang Zhan, Chang Jiang*
School of Electronics and Information Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China

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ժҪ ���һ�ֻ���DFT(Discrete Fourier Transforms)Ƶ����λ��Ϣ�����Ҳ�����߾��ȹ��Ʒ���.�÷���ͨ����ȡ���Ҳ������γ��Ȳ�ͬ����ɢ����,�������ǵ�DFTϵ������ȥ�����źŵ�Ƶ����,�Ӷ����������.ͬʱ,�������ڸ�˹������������,���ø��ַ����������Ҳ�������Ƶľ����������㹫ʽ,�˹�ʽ�����˾��������������ȼ�FFT(Fast Fourier Transforms)����֮��Ĺ�ϵ.���Դ˾����������С��ΪĿ��,�Ըù��Ʒ����������Ż��Ľ�,�õ������в���������ѡȡ����.ѡ�����Ų����Ĺ��̼��Ƕ��Ծ����������СΪĿ��������滮�����������.Ӧ��Monte Carlo����,���Ľ�����㷨�����������еļ��ֵ����㷨�����ܼ�Cramer-Rao���޽����˷����Ƚ�,����֤�����Ƶ��ľ����������㹫ʽ����ȷ��.
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Abstract�� A fast and accurate estimation technique of initial phase of single-tone signal based on the phase of discrete Fourier transforms (DFT) spectrum was proposed. The initial phase is obtained by removing the frequency item in the multinomial using the DFT coefficient which is from two discrete sinusoid signal sequences of different length. The root mean square error (RMSE) formula of initial phase estimation under Gaussian white noise was derived that presents the relationship among RMSE, fast Fourier transforms (FFT) length and signal noise ratio (SNR). The parameters in the formula were studied and optimized to minimize the RMSE. The process of which is to solve the integer programming problem with the objective function that RMSE is minimal. Through Monte Carlo simulation, the performance of the improved technique was compared with other typical algorithms and Cramer-Rao lower bound (CRLB), the RMSE formula is found to be effective.
Keywords�� phase measurement   discrete Fourier transforms   error analysis     
Received 2006-05-31;
About author: ���(1981-),��,������ɽ��,��ʿ��,lichunyu@ee.buaa.edu.cn.
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���, ������, ��չ, ����.����DFT�����Ҳ���������㷨��������[J]  �������պ����ѧѧ��, 2007,V33(05): 580-584
Li Chunyu, Zhang Xiaolin, Zhang Zhan, Chang Jiang.Phase estimation of sinusoid signal based on DFT and error analysis[J]  JOURNAL OF BEIJING UNIVERSITY OF AERONAUTICS AND A, 2007,V33(05): 580-584
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http://bhxb.buaa.edu.cn//CN/     ��     http://bhxb.buaa.edu.cn//CN/Y2007/V33/I05/580
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