Reconstruction of Periodic Band limited Signals from Non-uniform Samples

Digital Processing techniques are based on representing a continuous signal by a discrete set of samples. This process of reducing a continuous time signal to a discrete time signal is called sampling. There are a variety of applications in which the samples cannot be collected uniformly the data are known only on a nonuniformly spaced sampling set. In communication theory, when data from a uniformly sampled signal are lost, the result is generally a sequence of nonuniform samples. Nonuniform sampling is preferred over uniform sampling for sampling efficiency.The objective is to derive a closed-form algorithm (non-iterative) involving real-valued functions for reconstructing a periodic band limited signal from an even and an odd number of non-uniform samples. Non-uniform sampling comes natural in many applications, for example due to imperfect sensors, mismatched clocks or event-triggered phenomena. Applications can be found in automotive industry, mobile communication, medicine and astronomy.