Research On Iterative Algorithms For The Extrapolation Of Band-limited Function Based On Fast Fourier Transformation-Landweber

Extrapolation of Band-limited Function is widely used in many areas, such as signal recovery, radar signal synthesis, the design of radar antenna, medical tomographic imaging, the earthquake tomogtaphic imaging, astronomical objects imaging and so on. Although Band-limited signal is infinite in the time domain, we can just select a limited length in reality. So it is necessary to solve how to extrapolate to get infinite Band-limited signal based on a limited length signal. Extrapolation of Band-limited Function is important part in the research of incomplete data reconstruction. We can divide the algorithms for extrapolation of Band-limited function into three species, the first algorithm is based on continuous parsing, the second is based on series expansion, the last is based on constantly reduce the mean square error energy. But the three species have their own drawbacks, the first algorithm is unpractical, the second and the third are influenced by truncation errors. So some scholars in this domain Put forward new ideas and new algorithms about extrapolation of Band-limited function. That is research on iterative algorithms for the extrapolation of Band-limited function based on Fast Fourier Transformation. This paper is about the research on iterative algorithms for the extrapolation of Band-limited function based on Fast Fourier Transformation—Landweber.This algorithms not only extrapolate quickly and efficiently, but also still can get fairly accurate results when signal with noise. As long as select the location of the sample point and density properly, you can get preferable extrapolation performance and good spectrum estimation. Above all it can reduce the impacts by mix overlapping errors and truncation errors. Because this algorithm is with the help of FFT technology and it is not hard to determine convergence acceleration factor, so this algorithm is very practical.