FPGA implementations of fast Fourier transforms for real-time signal and image processing

Applications based on the fast Fourier transform (FFT), such as signal and image processing, require high computational power, plus the ability to experiment with algorithms. Reconfigurable hardware devices in the form of field programmable gate arrays (FPGAs) have been proposed as a way of obtaining high performance at an economical price. However, users must program FPGAs at a very low level and have a detailed knowledge of the architecture of the device being used. They do not therefore facilitate easy development of, or experimentation with, signal/image processing algorithms. To try to reconcile the dual requirements of high performance and ease of development, this paper reports on the design and realisation of a high level framework for the implementation of 1-D and 2-D FFTs for real-time applications. A wide range of FFT algorithms, including radix-2, radix-4, split-radix and fast Hartley transform (FHT) have been implemented under a common framework in order to enable the system designers to meet different system requirements. Results show that the parallel implementation of 2-D FFT achieves linear speed-up and real-time performance for large matrix sizes. Finally, an FPGA-based parametrisable environment based on 2-D FFT is presented as a solution for frequency-domain image filtering application.