A Fast and Accurate Method for Numerical Integration of Bandwidth-Limited Signals

Fast and accurate integration of images or signals is important in many applications. This paper reports a novel split-band integrator (SBI) that is especially suitable for integrating discrete images representing a bandwidth-limited signal sampled above its Nyquist frequency. The SBI combines the advantages of the classical Newton-Cotes formulas (NCFs) and a fast Fourier transform (FFT) based integrator while avoiding their drawbacks. It works by splitting an input into two images and processing them separately then combining the results, where one image containing high-frequency components is integrated using FFT, whereas the other collecting the remaining low-frequency portion is integrated accurately by a classical NCF. Both theoretical derivations and numerical tests are presented to demonstrate the SBI.