Research on the atomic clock signal denoising method based on the hyperbolic tangent smooth threshold function

To address the discontinuity and constant bias inherent in traditional hard and soft threshold functions, an atomicclock signal denoising method based on the hyperbolic tangent smooth threshold function was proposed. The atomicclock signal was decomposed into a series of intrinsic mode functions (IMFs) and a residual component usingempirical mode decomposition (EMD). A novel threshold function was constructed to achieve a continuous transitionbetween hard and soft threshold behaviors by introducing a smoothing factor. The optimal threshold for each IMFwas determined using Stein’s Unbiased Risk Estimate (SURE) criterion, and each IMF component was denoisedaccordingly. Finally, the denoised IMFs and the residual component were reconstructed to obtain the fi nal denoisedsignal. Case study analyses demonstrated that, in comparison with traditional wavelet threshold denoising methods,the proposed method suppressed noise eff ectively while preserving the smoothness and detailed features of thesignal more favorably. Specifi cally, in terms of noise suppression, the improved thresholding method increased theSNR by 14%, 5% and 26% for cesium clock, hydrogen clock and measured rubidium clock data. In terms of signalfi delity, its RMSE was reduced by 28%, 10% and 25% relative to the soft thresholding method. This method retainedthe authentic information of the signal while suppressing noise, and exhibited good repeatability. It eff ectivelyimproved the frequency stability of the time scale, thereby providing a novel technical approach for enhancing thequality of atomic clock data and the frequency stability of the time scale.