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

Time domain measurements are distorted by the measurement system if the bandwidth of the system is not sufficiently high compared to that of the signal to be measured. If the distortion is known the measured signal can be compensated 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 we can distinguish between systematic and stochastic errors. In this paper, we investigate the stochastic type of errors and suggest a method to calculate the uncertainty (variance) of the reconstruction. We developed a method for the calibration of high-speed sampling systems. Both stationary and jitter noises will be investigated.