https://hal.inria.fr/hal-01022989Bernal, DionisioDionisioBernalNortheastern University [Boston]On the Stability of Sequential DeconvolutionHAL CCSD2014Signal processingInverse problemsSource localization[PHYS.MECA] Physics [physics]/Mechanics [physics][SPI.MECA] Engineering Sciences [physics]/Mechanics [physics.med-ph][MATH.MATH-ST] Mathematics [math]/Statistics [math.ST][STAT.TH] Statistics [stat]/Statistics Theory [stat.TH]Jaigu, AnneLe Cam, Vincent and Mevel, Laurent and Schoefs, Franck2014-07-11 12:42:362014-07-11 13:29:512014-07-11 13:29:51enConference papersapplication/pdf1The time domain estimation of inputs from knowledge of the kernel and the outputs is a de-convolution operation. For finite dimensional systems treated in discrete time the operation is tantamount to solving a set of linear equations. When performing a deconvolution an issue that must be dealt with is the fact that the dimension of the system of equations grows with duration and becomes prohibitively large when the inputs are long. For this reason, and sometimes because it is of interest to estimate the inputs with the smallest possible delay, deconvolution must often be implemented on a moving window. This paper shows that a sequential deconvolution is a conditionally stable process and derives the expression that governs numerical stability.