Nonparametric Identification and Signal Reconstruction as two Consecutive Deconvolution Steps

Inverse filtering of time domain signals is investigated. Inverse filtering requires the knowledge of the transfer function of the measurement system, which can be estimated on the base of measurements (system identification). The quality of the system identification influences the quality of the signal reconstruction. We investigate the influence of the identification on the signal reconstruction in the case of ill-posed problems. It is shown that overfiltering the noise in the identification stage introduces bias in the pass- and transition region of the transfer function, which causes trouble in the signal reconstruction stage. Underfiltering the noise in the identification stage also causes bias, but its effect is mostly in the stopband, which can be suppressed in the signal reconstruction stage