Memory Optimized Re-gridding for Non-uniform Fast Fourier Transform on FPGAs

Abstract

Summary form only given. The Discrete Fourier Transform (DFT) can be viewed as the Fourier Transform of a periodic and regularly sampled signal as commonly defined in equation 1. The Non-Uniform Discrete Fourier Transform (NuDFT) is a generalization of the DFT for data that may not be regularly sampled in spatial or temporal dimensions. This flexibility allows for benefits in situation where sensor placement cannot be guaranteed to be regular or where prior knowledge of the informational content could allow for better sampling patterns than a regular one. NuDFT is used in applications such as Synthetic Aperture Radar (SAR), Computed Tomography (CT), and Magnetic Resonance Imaging (MRI). The NuDFT definition is shown in equation 2. Here the sample locations are points si in the set S. Each point, si has a complex value consisting of location or frequency components six and siy. The location or frequency components are, of course, not restriced to a discrete sampling grid.