Hi, Andrew, It's been a while since I've looked at the CASPER FFT implementation, but my understanding is that the "real" N-channel FFT actually packs two real FFTs into one 2N-channel complex FFT. Corresponding positive and negative bins of the complex FFT's output are added/subtracted to get the N channels for each of the two inputs. The "Nyquist channel" (channel +N or -N of the 2N complex FFT) has no corresponding channel and i think gets ignored in the current CASPER "real" FFT implementation (but not the complex FFT implementation).
The Nyquist channel is a bit of an oddity. The Fourier coefficients for that channel are all real (+1, -1, +1, -1...) so for a purely real (or imaginary) input the Nyquist channel will also be real (or imaginary). That means that the Nyquist channel of the two real inputs could easily (in theory) be separated. The idea Jonathan asks about (including the Nyquist channel's data in the imaginary component of the DC channel) is interesting, but due to aliasing the utility of that channel is somewhat diminished so I'm not sure how useful it would be. Dave > On May 22, 2017, at 02:13, Andrew Martens <and...@ska.ac.za> wrote: > > Hey Jonathon > > I am copying my reply to the list to expose my own potential ignorance. > > The CASPER FFT implements a DFT where each resultant bin is the same as > mixing with a complex exponential and then low pass filtering the result (as > per the DFT definition). The complex exponentials have frequencies centred at > 0, 2B/N, 2(2B/N) etc where B is the Bandwidth of your signal and N is the > number of FFT bins. So the 'DC' FFT bin goes from -(1/2)*(2B/N) to > (1/2)*(2B/N) or -B/N to B/N. For example, a signal sampled at 1024GS/s gives > a B of 512MHz. Assuming a 1k point FFT we have a 'DC' bin from -0.5MHz to > 0.5MHz. The N/2 FFT bin, in our example, contains 510.5MHz to 511.5MHz. So, > all of the FFT bins are shifted down by 1/2 bin from where you might > intuitively think they are located. Because we sample a real signal, and due > to aliasing, we discard the last N/2 FFT bins as they contain the same > information, but as shown above, they are not actually the same as the first > N/2. > > You probably know all of this but it does help answer your question. We > simply discard the last N/2 channels. So you can never get the last half an > FFT bin's worth of frequency info up to Nyquist (in our example, from > 511.5MHz to 512MHz. The DC bin is strange as it contains the aliased band > from 1023.5MHz to 1024 MHz (hopefully nicely filtered out in analogue > stages), as well as 0 MHz to 0.5MHz. So far, we have treated it as something > we throw away and have not tried to extract anything from it. > > This might be a problem for people wanting to do a very coarse FFT, as half > an FFT bin might be a lot of bandwidth to discard. > > Regards > Andrew > > On Fri, May 19, 2017 at 6:17 PM, Jonathon Kocz <jxk...@gmail.com > <mailto:jxk...@gmail.com>> wrote: > Hi Andrew, > > Sorry to bug you, but I thought it was easier to ask first before looking at > the FFT in detail. > > Do you remember, in the CASPER FFT, is the Nyquist frequency (the purely > imaginary ch N/2 + 1) put in the imaginary part of the DC or discarded? > > Cheers, > Jonathon > > > -- > You received this message because you are subscribed to the Google Groups > "casper@lists.berkeley.edu" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to casper+unsubscr...@lists.berkeley.edu > <mailto:casper+unsubscr...@lists.berkeley.edu>. > To post to this group, send email to casper@lists.berkeley.edu > <mailto:casper@lists.berkeley.edu>. -- You received this message because you are subscribed to the Google Groups "casper@lists.berkeley.edu" group. To unsubscribe from this group and stop receiving emails from it, send an email to casper+unsubscr...@lists.berkeley.edu. To post to this group, send email to casper@lists.berkeley.edu.
