Hi Stevo, The short answer is that there aren't any papers I know of that went into more detail on the math (I certainly didn't write one). However, the decomposition of a large FFT into smaller FFTs is a standard property of the the radix-2 (and generally, radix-N) FFT algorithm.
The reordering and phase shifting is absolutely necessary to preserve the phase relationships between all the various frequencies in the band. Aaron On Thu, Jun 19, 2014 at 2:10 PM, Stevo Bailey < [email protected]> wrote: > Hi CASPERians, > > I'm working on a digital ASIC spectrometer like the Splash > <https://casper.berkeley.edu/wiki/PIDDP_Spectrometer> one, but > constructed in Chisel <https://chisel.eecs.berkeley.edu/> instead of the > CASPER tools. Thus I'm implementing a number of DSP algorithms from > scratch. I'm trying to work out the math behind a large-point FFT block. > From my understanding, it consists of a number of biplex pipelined FFTs in > parallel, followed by some reordering or phase shifting (is this > necessary?), then followed by an in-place FFT. I have the biplex FFTs done. > I'm looking for documents or publications discussing the math behind > combining the parallel FFT results for the in-place FFT. Aaron has a paper > <http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4840623> on > this, but I was hoping for one with more detail. > > Thanks! > Stevo > -- Aaron Parsons 510-306-4322 Hearst Field Annex B54, UCB
