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Accurate and fast discrete polar Fourier transform

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5 Author(s)
A. Averbuch ; CS Dept., Tel Aviv Univ., Israel ; R. R. Coifman ; D. L. Donoho ; M. Elad
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In this article we develop a fast high accuracy polar FFT. For a given two-dimensional signal of size N×N, the proposed algorithm's complexity is O(N2 log N), just like in a Cartesian 2D-FFT. A special feature of our approach is that it involves only 1-D equispaced FFT's and 1D interpolations. A central tool in our approach is the pseudopolar FFT, an FFT where the evaluation frequencies lie in an over-sampled set of nonangularly equispaced points. The pseudopolar FFT plays the role of a halfway point-a nearly-polar system from which conversion to polar coordinates uses processes relying purely on interpolation operations. We describe the conversion process, and compare accuracy results obtained by unequally-sampled FFT methods to ours and show marked advantage to our approach.

Published in:

Signals, Systems and Computers, 2004. Conference Record of the Thirty-Seventh Asilomar Conference on  (Volume:2 )

Date of Conference:

9-12 Nov. 2003