This method solves the dual problem of blind deconvolution and estimation of the time waveform of noisy second-order cyclo-stationary (CS2) signals that traverse a Transfer Function (TF) en route to a sensor. We have proven that the deconvolution filter exists and eliminates the TF effect from signals whose statistics vary over time. This method is blind, meaning it does not require prior knowledge about the signals or TF. Simulations demonstrate the algorithm high precision across various signal types, TFs, and Signal-to-Noise Ratios (SNRs). In this study, the CS2 signals family is restricted to the product of a deterministic periodic function and white noise. Furthermore, this method has the potential to improve the training of Machine Learning models where the aggregation of signals from identical systems but with different TFs is required.

翻译：该方法解决了带有噪声的二阶循环平稳（CS2）信号在通过传递函数（TF）传输至传感器过程中的盲反卷积与时域波形估计这一对偶问题。我们已证明，对于统计特性随时间变化的信号，反卷积滤波器存在且能消除传递函数的影响。该方法是盲的，即无需事先了解信号或传递函数的先验知识。仿真结果表明，该算法在各种信号类型、传递函数及信噪比（SNR）条件下均具有高精度。本研究中，CS2信号族被限定为确定性周期函数与白噪声的乘积。此外，该方法有望改进机器学习模型的训练，其中需要聚合来自同一系统但具有不同传递函数的信号。