The Optimum Approximation of Signals That Have Small Side-Lobes Bounded By A Measure Like Kullback-Leibler Divergence

摘要

We present the optimum running approximation of band-limited signals using sample values of outputs of FIR analysis filters. We consider set of signals with a main-lobe and a pair of small side-lobes. We assume that weighted square-integral of the main-lobe is bounded. Further, for the purpose of denning divergence of side-lobes of error in attenuation band, we introduce a measure like Kullback-Leibler divergence and assume that this measure is bounded. Finally, we prove that the presented approximation minimizes various measures of error at the same time.