Peak value estimation of bandlimited signals from their samples, noise enhancement, and a local characterization in the neighborhood of an extremum

The paper addresses the problem of estimating the peak value of bandlimited signals from their samples with and without oversampling. This problem has significant relevance to orthogonal frequency-division multiplexing (OFDM) signal processing and system design. In particular, an upper bound on the peak value is established given the peak value of the samples and the oversampling rate. Moreover, it is shown that the bounds are sharp for all practical rates by constructing bandlimited signals taking on this bound. The proof also provides a local characterization of bandlimited signals in the neighborhood of an extremum. A different analysis examines the effect of small errors in the samples. It is shown that oversampling can provide robust recovery in the sense that small errors in the samples lead to small errors in the reconstructed signal. Again, an upper bound is derived relating the peak error in the samples and the peak error in the signals. Furthermore, both problems are shown to be coupled and put in a unifying context. The bounds are compared and applied to problems concerning OFDM.