An improved fast Fourier transform in polar coordinate system

Abstract

The problem of calculating the discrete Fourier transform (DFT) acquired in polar coordinate system has been given considerable attention in many fields during the last 40 years such as antenna, image registration, tomography. etc. Unlike DFT, the discrete polar Fourier transform (DPFT) has no X-Y separability and can't be directly computed by fast Fourier transform (FFT). This paper proposes an improved fast DPFT algorithm aiming at 2D real array data. By utilizing the properties of the shift discrete Fourier transform (SDFT) and the chirp-Z transform (CZT), the algorithm's overall computational complexity is significantly decreased and is more suitable for real-time applications by only 1D calculations. The experimental results demonstrate the applicability and good performance of this approach.