Using divide-and-conquer on custom lengthened Fourier transforms

Fourier transforms (FTs) are the key to all modern, OFDM-based (orthogonal frequency division multiplexing) transmission schemes. This paper demonstrates the principles and the efficient implementation of arbitrary length FTs, using divide and conquer techniques for decomposition into "atomic" transforms. Using "digital radio mondiale" as an example, we present generalized FT processing hardware, its complexity, processing time, precision and design re-use.