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1999•IEEE Transactions on Signal ProcessingRequires access

Reconstruction of a compactly supported function from the discrete sampling of its Fourier transform

Jiahong Yin, A.R. De Pierro, Musheng Wei

Open publisher page 11 citations

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.

About this research paper

What this paper is about

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.

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OpenAlex reports 11 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

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Method / approach

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Available 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.

Key concepts: Discrete-time Fourier transform, Discrete Fourier transform (general), Non-uniform discrete Fourier transform, Fourier transform, Fractional Fourier transform, Window function, Mathematics, Discrete Fourier series

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