Recursive Fourier Transform hardware

The Discrete Fourier Transform has played a fundamental role in signal analysis for radar systems, usually in its Fast Fourier Transform form. Traditionally, samples from a region of interest have been acquired, and processed in a block-processing fashion. The result is a delayed output equal to the time taken to acquire the data and then perform the Fourier Transform. To overcome this limitation, this work focuses on the development of a parallel framework for the execution of the Discrete Fourier Transform using a recursive algorithm, using many simple processing elements. The Fourier coefficients are updated every time a new sample is presented to the system, with a small latency. The system described in this work shows a 64 point Discrete Fourier Transform computation in parallel, which achieves a throughput of 817MSPS(29.42Gbit/s). The framework proposed promotes adjustable parallelism using the many simple processing elements. We show the engine is capable of dynamically correcting accumulated errors due to finite arithmetic, and allows simple adoption on existing systems.