Hi Again!, I've been trying to setup the technique you use. I programmed what you said in matlab, generated a corner turn after the first PFB+FFT writing the spectra row wise, and then feed the second FFT with the data of the Corner Turner column wise. But what i see in the final spectra is not like a real spectra, because for example when i analyze a signal in time with a certain frequency, then i see two tones in the spectra instead of two. this two tones are far away N2 (where N2 is the size of the second FFT) channels always. Another issue is that this two tones are always on the DC channel of adjacent spectra of the second FFT.
I try to understand the concept you tried to explain. You are exploiting the fact that each channel of the PFB is like a narrow filter that extract information of the signal in a narrow bandwidth BW/1024 width . So then you Fourier transform 1024 values (each one representing the same channel of the PFB) to generate the spectra of the BW/1024 bandwidth. Am I correct? the problem i have is that the data at the output of the first PFB+FFT is in the frequency domain, so i don't see the time series or the time domain signal. So how could you get the time series you told me? thanks in advance. 2014-10-10 11:03 GMT-04:00 Danny Price <[email protected]>: > Hi Edguardo > > If I recall right, the tutorial is a 2048 point real PFB + FFT (1024 > channels), a 1024x1024 corner turn, and then a 1024 point complex FFT to > give 1M channels. You are right that this isn't exactly the same as a 1M > point FFT. The main difference you'll see is scalloping on the edge > channels, a tooth-like pattern repeating every 1024 channels that arises > due to the filter response of the first FFT. > > To explain, this is essentially a clever implementation of a "zoom FFT", > where you select a single channel, form a time series from it, and then > compute another FFT on the time series. Zoom FFTs work as each channel of > an FFT can be thought of as a critically-sampled filter (with complex > output). > > If you think of a single channel, the first FFT filters and downsamples by > a factor of 1/1024. We then buffer up 1024 channels, and feed it to a > second FFT, and get very fine channel resolution. The sneaky part is that > as this is implemented on an FPGA, the second FFT is free for 1023/1024 > clock cycles. So, we can use the second FFT multiple times for free -- the > corner turn arranges data so that we can continually pump in more data, > getting 1024x1024 channels in total. > > Hope that makes sense! > > - Danny > >> Edgardo Huaracán Durán <mailto:[email protected]> >> October 10, 2014 at 10:25 AM >> >> Hi all, >> >> I’m trying to understand the approach you use in the 1 M channel tutorial >> situated in the old tutorial link (https://casper.berkeley.edu/ >> wiki/Old_Tutorials) called high resolution spectrometer. >> >> I've take a look at other similar implementations like ''A 6*320-MHz >> 1024-Channel FFT Cross-Spectrum Analyzer for Radio Astronomy'' ( >> http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=1458140), where they >> use the corner turner technique. Basically they implement the Cooley-Tukey >> FFT algorithm to have a large DFT coming from two smaller DFT. They use a >> first stage of corner turner previous to the first DFT and acumulate time >> samples column wise, to then enter to the First DFT row wise. There is >> another corner turner stage at the output of the First DFT and after >> twiddle factor multiplications the data is input again to another DFT. >> >> I understand the mathematics behind the above text, but seems to me that >> the approach used on your 1 MChannel Spectrometer is a little different >> from that treatment. I can't find the twiddle factors in your model and >> also you use just one corner turner stage instead of two. So i'm not able >> to understand how your tutorial works in a mathematical or theoretical >> sense. >> >> Could you give me an advice? where can i find a document to have more >> details? >> >> >> Thanks in advance. >> >> -- >> /Edgardo Huaracán Durán/ >> / >> / >> /Observatorio Astronómico Nacional >> / >> / >> Universidad de Chile/ >> >> -- *Edgardo Huaracán Durán* *Departamento de AstronomíaUniversidad de Chile* http://www.das.uchile.cl/lab_mwl/people.html
