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：本方法解决了含噪二阶循环平稳（CS2）信号在通过传递函数（TF）到达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够消除TF效应。该方法具有盲性，即无需预先了解信号或TF的相关信息。仿真结果表明，该算法在不同信号类型、传递函数及信噪比（SNRs）下均能达到高精度。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，该方法有望改善需要对来自同一系统但具有不同TF的信号进行聚合的机器学习模型的训练效果。