Frequency estimation for underwater CW pulse by interpolation on fractional Fourier coefficients based on amplitude ratio method

Fast and accurate estimation of sinusoidal signals plays an important role in many fields like communications, radar, sonar, etc. In underwater signal processing applications, sinusoidal signals usually take the form of CW pulses in most practical applications, therefore, zero-padding and duty-cycle show their great importance to the estimation of sinusoidal signals. In this paper, a high-precision estimation algorithm of sinusoidal signal is proposed, which combines amplitude ratio algorithm and fractional Fourier coefficient interpolation algorithm. The proposed algorithm uses the adjacent spectral line ratio algorithm instead of the Fourier coefficient maximum amplitude discrete spectral line search algorithm for coarse estimation, and modifies the traditional interpolation method. The proposed algorithm improves the Fourier coefficient interpolation algorithm by combining zero-padded signals to achieve the accurate frequency estimation for zero-padded sinusoidal signal. The performance of the algorithm is also in accordance with theoretical level for zero-padded signals, which is a great improvement over the frequency estimation algorithm for non-padded signals as well as the algorithm for zero-padding signals. The theoretical results are verified by extensive computer simulations which show that the proposed algorithm can both achieve better results for zero-padding cases and maintain comparable performance with competing algorithms for the non-padded signal. Therefore, the algorithm can be better applied to practical underwater detection or communication signals.