An Eigenvalue Decomposition Based Amplitude Extraction Method for EIT Demodulation System

This work presents an amplitude extraction method based on eigenvalue decomposition (EVD), which can substitute the role of phase-sensitive demodulation in electrical impedance tomography (EIT) demodulation systems. An m
$\times $
m square signal matrix is initially constructed according to a series of samples and an m
$\times $
n Hankel matrix. Then, the EVD operation is performed on the square signal matrix, and as a result, its eigenvalues are sequentially obtained. Finally, a mathematical relation among the sinusoid amplitude, effective eigenvalues and the number of rows of the constructed signal matrix is provided. Compared to traditional methods, the proposed method offers the following merits: 1) since no reference signal is required, there is no need to consider synchronization between the received and reference signals; 2) it can extract the signal amplitude with high signal-to-noise ratio (SNR), even in the case of non-integer periodic sampling; 3) EVD itself can achieve a filtering function, thereby additional low-pass filters are unnecessary for the signal conditioning module. The feasibility and accuracy of the proposed method are verified by simulations and experimental results, demonstrating that it can provide the amplitude information with excellent robustness and SNR performances.