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.
Jain V K, Collins W L, Davis D C. High-accuracy analog measurements via interpolated FFT [J]. IEEE Trans on IM, 1979, 28 (2):113-122
Dusan Agrez. Improving phase estimation with leakage minimization [J]. IEEE Trans on IM, 2005,54(4):1347-1353
�����,������. ����DFT��λ�����Ҳ�Ƶ�ʺͳ���ĸ߾��ȹ��Ʒ���[J]. ����ѧ��,2001,29(9):1164-1167 Qi Guoqing, Jia Yule. High-accuracy frequency and phase estimation of single-tone based on phase of DFT [J]. Acta Electronica Sinica, 2001, 29(9):1164-1167(in Chinese)
����. ���Ҳ�Ƶ�ʿ��ٹ��Ʒ���[J]. ���ݲɼ��봦��, 1998, 13(1):8-11 Liu Yu. Fast frequency estimation of single tone [J]. Journal of Data Acquisition & Processing, 1998, 13(1):8-11 (in Chinese)
����. ���ٸ߾������Ҳ�Ƶ�ʹ����ۺ��㷨[J]. ����ѧ��,1999,27(6):126-128 Liu Yu. A fast and accurate single frequency estimator synthetic approach [J]. Acta Electronica Sinica, 1999,27(6):126-128 (in Chinese)
Rife D C, Boorstyn P R. Single tone parameter estimation from discrete-time observations [J]. IEEE Trans Info Theory, 1974, IT-20(5):591-598
Christ D Richmond. On the probability of resolution for the amplitude and phase estimation (APES) spectral estimation The 30th International Conference on Acoustics, Speech, and Signal Processing (ICASSP2005). Philadelphia, USA:IEEE, 2005:iv/1025 - iv/1028