Accurate and fast discrete polar fourier transform

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.