Minimax Approximation of Representation Coefficients From Generalized Samples

Many sources of information are of analog or continuous-time nature. However, digital signal processing applications rely on discrete data. We consider the problem of approximating L₂ inner products, i.e., representation coefficients of a continuous-time signal, from its generalized samples. Adopting a robust approach, we process these generalized samples in a minimax optimal sense. Specifically, we minimize the worst approximation error of the desired representation coefficients by proper processing of the given sample sequence. We then extend our results to criteria which incorporate smoothness constraints on the unknown function. Finally, we compare our methods with the piecewise-constant approximation technique, commonly used for this problem, and discuss the possible improvements by the suggested schemes.