Accurate and fast discrete polar fourier transform

A. Averbuch*, R. R. Coifman, D. L. Donoho, M. Elad, M. Israeli

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

Abstract

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(N 2 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 pseudo-polar FFT, an FFT where the evaluation frequencies lie in an over-sampled set of non-angularly equispaced points. The pseudo-polar 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.

Original languageEnglish
Pages (from-to)1933-1937
Number of pages5
JournalConference Record of the Asilomar Conference on Signals, Systems and Computers
Volume2
StatePublished - 2003
EventConference Record of the Thirty-Seventh Asilomar Conference on Signals, Systems and Computers - Pacific Grove, CA, United States
Duration: 9 Nov 200312 Nov 2003

Fingerprint

Dive into the research topics of 'Accurate and fast discrete polar fourier transform'. Together they form a unique fingerprint.

Cite this