Uncertainty of signal reconstruction in the case of jittery and noisy measurements

Time domain measurements are distorted by the measurement system if the ban dwidth of the system is not sufficiently high compared to that of the signa l to be measured. If the distortion is known the measured signal can be com pensated for it (inverse filtering or deconvolution), Since the measurement is always corrupted by noise, the reconstruction is an estimation task, i. e., the reconstructed signal may vary depending on the actual noise record. Our aim is to investigate the errors related to the signal reconstruction, and to provide an error bound around the reconstructed time domain waveform . Based on their nature rye can distinguish between systematic and stochast ic errors. In this paper, we investigate the stochastic type of errors and suggest a method to calculate the uncertainty (variance) of the reconstruct ion. We developed a method for the calibration of high-speed sampling systems. B oth stationary and jitter noises will be investigated.