Analysis and recovery of sample-and-hold and linearly interpolated signals with irregular samples

A modular method is suggested to recover a bandlimited signal from the sample-and-hold and linearly interpolated (or, in general, an nth-order hold) version of the irregular samples. The approach is an extension of work for the sample-and-hold signals with uniform samples. A coordinate transform technique is applied to show a practical way of finding an approximate inverse coordinate mapping. As a byproduct, some sufficient conditions on the nonuniform samples for the modular technique to the valid are derived.>