Deconvolution and Total Least Squares in Finding the Impulse Response of an Electromagnetic System from Measured Data

Total least squares (TLS) is a method of solving overdetermined sets of (linear equations AX ≈ b when there are errors both in the observation vector b (m × 1) and in the data matrix A (m × n). This method is particularly useful when the data matrix A is singular or highly ill conditioned. We present the method of finding the TLS by applying the singular value decomposition to the discrete deconvolution problem. Numerical results are presented for finding the impulse response of a transmission line from experimental data. The advantage of this approach is that this method can be automated based on the signal to noise ratio of the measured data.