L2 signal reconstruction with FIR and steady-state behavior constraints

The problem of recovering an analog signal from discrete measurements, known as signal reconstruction, can be formulated as a sampled-data L² fixed-lag smoothing problem. In this paper the problem is solved under the constraint that the reconstructor is an FIR (finite impulse response) system. An analytic and numerically stable solution, whose computational complexity is linear in the length of the reconstructor impulse response, is derived. The formulation can accommodate steady-state constraints via the use of weights with imaginary axis eigenvalues and imposing the stability requirement on the error system.