System Impulse Response Estimation Using Reconstructive Algorithms

Abstract

Estimating the impulse response of linear systems from undersampled measurements is of particular interest in monitoring applications constrained by hardware and sampling resources. This contribution presents a compressed sensing-based approach employing wide-band pseudo-random binary sequence excitation to estimate the impulse response of linear systems. The reconstruction problem is formulated as sparse recovery and solved using greedy algorithms, namely Orthogonal Matching Pursuit and Iterative Hard Thresholding, and evaluated on four passive filter topologies. The method is assessed using the root-mean-square error metric in the frequency domain. The results demonstrate stable reconstruction performance at sampling frequencies up to eight times lower than the Nyquist frequency corresponding to the symbol rate of the excitation signal. The influence of reconstruction length, sparsity level, and compression ratio on identification accuracy and robustness is systematically analysed, identifying a stable operating region and clarifying the trade-off between reconstruction fidelity and measurement reduction for practical implementation.