Title :
Reconstruction of a compactly supported function from the discrete sampling of its Fourier transform
Author :
Yin, Jiahong ; De Pierro, Alvaro R. ; Wei, Musheng
Author_Institution :
Dept. of Appl. Math., State Univ. of Campinas, Brazil
fDate :
12/1/1999 12:00:00 AM
Abstract :
We derive a new relation between the discrete Fourier transform of a discrete sampling set of a compactly supported function and its Fourier transform. From this relation, we obtain a new window function. We then propose a new efficient algorithm to reconstruct the original function from the discrete sampling of its Fourier transform, which can adopt the fast Fourier transform and has much better accuracy than those in the literature. Several numerical experiments are also provided, illustrating the results
Keywords :
discrete Fourier transforms; filtering theory; signal reconstruction; signal sampling; Fourier transform; compactly supported function reconstruction; discrete Fourier transform; discrete sampling; efficient algorithm; fast Fourier transform; filtering approach; numerical experiments; signal processing; window function; Discrete Fourier transforms; Fast Fourier transforms; Filters; Fourier series; Fourier transforms; Helium; Interpolation; Mathematics; Sampling methods; Signal processing algorithms;
Journal_Title :
Signal Processing, IEEE Transactions on