Fast Solutions to Real-Data Discrete Fourier Transform

Abstract

This chapter discusses the two approaches conventionally adopted for dealing with the real-data DFT problem. The first approach involves the design of specialized fast algorithms, such as those due to Bergland and Bruun, which are geared specifically to addressing real-data applications and therefore able to exploit, in a direct way, the real-valued nature of the data – which is known to result in a Hermitian-symmetric frequency spectrum. The second approach, which is the most commonly adopted, particularly for applications requiring a hardware solution, involves re-structuring the data so as to use an existing complex-data FFT algorithm, possibly coupled with pre-FFT and/or post-FFT stages, to produce the DFT of either one or two (produced simultaneously) real-valued data sets – such solutions thus said to be obtained via a “real-from-complex” strategy. A discussion is finally provided relating to the results obtained in the chapter.