Conventionally, the Fast Fourier Transform (FFT) has been adopted over the Discrete Fourier Transform (DFT) due to its faster execution. However, the emergence of modern high performance computing devices has favored the DFT algorithm due to its inherent parallelism. This letter explores a straightforward one-dimensional DFT whose performance is evaluated against the NVIDIA and AMD’s highly optimized FFT libraries, cuFFT and clFFT, respectively. Performance is analyzed in terms of average kernel execution time for data ranging from 21 to 225 samples across the NVIDIA GeForce GTX 1080 Ti and AMD Radeon RX 6800 XT graphical processors. The DFT algorithm achieves comparable results to the FFT routines for smaller input sizes whereas it significantly outperforms the FFT libraries for larger input lengths. The DFT shows an average performance increase of 177.7% over the cuFFT on the NVIDIA GeForce device using the CUDA toolkit. For the AMD Radeon graphical processor, the DFT outperforms the clFFT by an average of 184.2% using the OpenCL specification.

Time-domain back projection (BP) is a widely known method used in Synthetic Aperture Radar (SAR) image formation. Despite its advantages over other image formation algorithms, the BP method is hindered due to its computational complexity and its requirement of higher number of operations and processing power. Recently, Field Programmable Gate Array (FPGA) devices have been used for BP acceleration mainly due to their parallel processing capabilities, reconfigurability, scalability, and low power requirement. This paper presents a new Fixed-point based BP (FxBP) design for FPGA devices and a Floating-point based BP (FlBP) design to compare performance. Both designs are developed with N-Dimensional Range (NDR) structure and Single Work Item (SWI) structure using OpenCL. The FPGA performance is evaluated using a FPGA performance metric (FPM). It is shown that FxBP-NDR and FxBP-SWI designs generate high quality back projected images compared to FlBP designs, while saving 16.87 % and 42.54 % on logic resources and gaining 17.90 % and 91.62 % on FPGA performance in NDR and SWI, respectively. Obtained results clearly indicate that FPGA devices perform significantly better with FxBP designs compared to FlBP designs, even with hardened FPUs.