Estimation of sequences in a signal class determined from the data

An algorithm is presented for extrapolation and spectral estimation of discrete-time signals from a set of samples. First, we assume the given samples are those of a length N sequence that is a member of a signal class consisting of the collection of outputs of a known filter with limited-energy inputs. Then we estimate by finding the signal that goes through the samples and which gives the best estimate of an arbitrary time or frequency sample using a minmax criterion. This estimate is linear and optimal over all the signals in the class and over all possible data. Next we obtain a series of signal estimates, each of which assumes the signal belongs to a different class. We make these classes depend on the data recursively by re-defining them using the previous signal estimate. Convergence of the algorithm is discussed and an example is provided to illustrate the technique.