So, there are algorithms out there to perform an FFT on real data, that save (I think) roughly 2x the calculations of FFTs for complex data. I did a quick search, but didn't find any that are made specifically for FPGAs. Was my search too quick, or are there no IP sources to do this? It would seem like a slam-dunk for Xilinx and Intel/Altera to include these algorithms in their FFT libraries. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com I'm looking for work -- see my website!
All-real FFT for FPGA
Started by ●February 12, 2017
Reply by ●February 12, 20172017-02-12
On Sunday, February 12, 2017 at 12:05:25 PM UTC-6, Tim Wescott wrote:> So, there are algorithms out there to perform an FFT on real data, that > save (I think) roughly 2x the calculations of FFTs for complex data. > > I did a quick search, but didn't find any that are made specifically for > FPGAs. Was my search too quick, or are there no IP sources to do this? > > It would seem like a slam-dunk for Xilinx and Intel/Altera to include > these algorithms in their FFT libraries. > > -- > > Tim Wescott > Wescott Design Services > http://www.wescottdesign.com > > I'm looking for work -- see my website!It's been a long time, as I remember: The Hartley transform will work. Shuffling the data before and after a half size complex FFT will work. And you can use one of them to check the other.
Reply by ●February 12, 20172017-02-12
On 2/12/2017 1:05 PM, Tim Wescott wrote:> So, there are algorithms out there to perform an FFT on real data, that > save (I think) roughly 2x the calculations of FFTs for complex data. > > I did a quick search, but didn't find any that are made specifically for > FPGAs. Was my search too quick, or are there no IP sources to do this? > > It would seem like a slam-dunk for Xilinx and Intel/Altera to include > these algorithms in their FFT libraries.I thought I replied to this, but my computer has been crashing a bit so maybe I lost that one. An FFT is inherently a complex function. Real data can be processed by taking advantage of some of the symmetries in the FFT. I don't recall the details as it has been over a decade since I worked with this, but you can fold half of the real data into the imaginary portion, run a size N/2 FFT and then unfold the results. I believe you have to run a final N sized complex pass on these results to get your final answer. I do recall it saved a *lot* when performing FFTs, nearly 50%. -- Rick C
Reply by ●February 13, 20172017-02-13
On Sun, 12 Feb 2017 20:32:59 -0500, rickman wrote:> On 2/12/2017 1:05 PM, Tim Wescott wrote: >> So, there are algorithms out there to perform an FFT on real data, that >> save (I think) roughly 2x the calculations of FFTs for complex data. >> >> I did a quick search, but didn't find any that are made specifically >> for FPGAs. Was my search too quick, or are there no IP sources to do >> this? >> >> It would seem like a slam-dunk for Xilinx and Intel/Altera to include >> these algorithms in their FFT libraries. > > I thought I replied to this, but my computer has been crashing a bit so > maybe I lost that one. > > An FFT is inherently a complex function. Real data can be processed by > taking advantage of some of the symmetries in the FFT. I don't recall > the details as it has been over a decade since I worked with this, but > you can fold half of the real data into the imaginary portion, run a > size N/2 FFT and then unfold the results. I believe you have to run a > final N sized complex pass on these results to get your final answer. I > do recall it saved a *lot* when performing FFTs, nearly 50%.My understanding is that there were some software packages that baked that into the algorithm, for what savings I don't know. I was wondering if it was done for FFTs as well. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com I'm looking for work -- see my website!
Reply by ●February 13, 20172017-02-13
On 2/12/2017 1:05 PM, Tim Wescott wrote:> So, there are algorithms out there to perform an FFT on real data, that > save (I think) roughly 2x the calculations of FFTs for complex data.> I did a quick search, but didn't find any that are made specifically for > FPGAs. Was my search too quick, or are there no IP sources to do this?> It would seem like a slam-dunk for Xilinx and Intel/Altera to include > these algorithms in their FFT libraries.Protip: the synthesizer should trim out the unneeded logic, so you don't need an optimized library macro. Steve, always helpful
Reply by ●February 13, 20172017-02-13
On 2/13/2017 12:03 AM, Tim Wescott wrote:> On Sun, 12 Feb 2017 20:32:59 -0500, rickman wrote: > >> On 2/12/2017 1:05 PM, Tim Wescott wrote: >>> So, there are algorithms out there to perform an FFT on real data, that >>> save (I think) roughly 2x the calculations of FFTs for complex data. >>> >>> I did a quick search, but didn't find any that are made specifically >>> for FPGAs. Was my search too quick, or are there no IP sources to do >>> this? >>> >>> It would seem like a slam-dunk for Xilinx and Intel/Altera to include >>> these algorithms in their FFT libraries. >> >> I thought I replied to this, but my computer has been crashing a bit so >> maybe I lost that one. >> >> An FFT is inherently a complex function. Real data can be processed by >> taking advantage of some of the symmetries in the FFT. I don't recall >> the details as it has been over a decade since I worked with this, but >> you can fold half of the real data into the imaginary portion, run a >> size N/2 FFT and then unfold the results. I believe you have to run a >> final N sized complex pass on these results to get your final answer. I >> do recall it saved a *lot* when performing FFTs, nearly 50%. > > My understanding is that there were some software packages that baked > that into the algorithm, for what savings I don't know. I was wondering > if it was done for FFTs as well.I'm not sure what you mean. When you say "baking" it into the algorithm, it would do pretty much what I described. That *is* the algorithm. I haven't heard of any other optimizations. The savings is in time/size. Essentially it does an N/2 size FFT with an extra pass, so instead of N*log(N) step it takes (N+1)*log(N/2) steps. -- Rick C
Reply by ●February 13, 20172017-02-13
On 2/13/2017 1:48 AM, rickman wrote:> On 2/13/2017 12:03 AM, Tim Wescott wrote: >> On Sun, 12 Feb 2017 20:32:59 -0500, rickman wrote: >> >>> On 2/12/2017 1:05 PM, Tim Wescott wrote: >>>> So, there are algorithms out there to perform an FFT on real data, that >>>> save (I think) roughly 2x the calculations of FFTs for complex data. >>>> >>>> I did a quick search, but didn't find any that are made specifically >>>> for FPGAs. Was my search too quick, or are there no IP sources to do >>>> this? >>>> >>>> It would seem like a slam-dunk for Xilinx and Intel/Altera to include >>>> these algorithms in their FFT libraries. >>> >>> I thought I replied to this, but my computer has been crashing a bit so >>> maybe I lost that one. >>> >>> An FFT is inherently a complex function. Real data can be processed by >>> taking advantage of some of the symmetries in the FFT. I don't recall >>> the details as it has been over a decade since I worked with this, but >>> you can fold half of the real data into the imaginary portion, run a >>> size N/2 FFT and then unfold the results. I believe you have to run a >>> final N sized complex pass on these results to get your final answer. I >>> do recall it saved a *lot* when performing FFTs, nearly 50%. >> >> My understanding is that there were some software packages that baked >> that into the algorithm, for what savings I don't know. I was wondering >> if it was done for FFTs as well. > > I'm not sure what you mean. When you say "baking" it into the > algorithm, it would do pretty much what I described. That *is* the > algorithm. I haven't heard of any other optimizations. The savings is > in time/size. Essentially it does an N/2 size FFT with an extra pass, > so instead of N*log(N) step it takes (N+1)*log(N/2) steps.Opps, I wrote that wrong. The optimized result would be order N/2 * (log(N)+1). Just to be clear (or less clear depending on how you read this), there are actually N/2 butterflies in each pass of the FFT. I didn't show that since the constant 1/2 applies to both the standard FFT and the optimized FFT. The point is the number of butterflies is cut in half on each pass of the FFT for the optimized approach. -- Rick C
Reply by ●February 13, 20172017-02-13
On 2/13/2017 12:24 AM, Steve Pope wrote:> On 2/12/2017 1:05 PM, Tim Wescott wrote: > >> So, there are algorithms out there to perform an FFT on real data, that >> save (I think) roughly 2x the calculations of FFTs for complex data. > >> I did a quick search, but didn't find any that are made specifically for >> FPGAs. Was my search too quick, or are there no IP sources to do this? > >> It would seem like a slam-dunk for Xilinx and Intel/Altera to include >> these algorithms in their FFT libraries. > > Protip: the synthesizer should trim out the unneeded logic, so > you don't need an optimized library macro.I don't think the synthesizer is capable of getting the same savings. The optimizations would see the zero imaginary inputs and optimize the first pass of the FFT. All passes would be N/2 butterflies while the optimized approach would use half that many at the expense of an extra pass. This is a big savings that the synthesis tools aren't likely to figure out unless they recognize you are performing an FFT. Someone refresh my memory. If you do an FFT with zeros in the imaginary part of the inputs, the output has a symmetry that can be used to process two real streams at once. I can't recall how it works exactly, but that symmetry is the basis for separating the results of the two halves of the original sequence before completing the last pass. One portion is pulled out because of the even symmetry and the other portion is pulled out because of the odd symmetry. I found this page that appears to explain it, but I haven't taken the time to dig into the math. I think I'd have to start all over again, it's just been too long. -- Rick C
Reply by ●February 13, 20172017-02-13
On Mon, 13 Feb 2017 01:48:49 -0500, rickman wrote:> On 2/13/2017 12:03 AM, Tim Wescott wrote: >> On Sun, 12 Feb 2017 20:32:59 -0500, rickman wrote: >> >>> On 2/12/2017 1:05 PM, Tim Wescott wrote: >>>> So, there are algorithms out there to perform an FFT on real data, >>>> that save (I think) roughly 2x the calculations of FFTs for complex >>>> data. >>>> >>>> I did a quick search, but didn't find any that are made specifically >>>> for FPGAs. Was my search too quick, or are there no IP sources to do >>>> this? >>>> >>>> It would seem like a slam-dunk for Xilinx and Intel/Altera to include >>>> these algorithms in their FFT libraries. >>> >>> I thought I replied to this, but my computer has been crashing a bit >>> so maybe I lost that one. >>> >>> An FFT is inherently a complex function. Real data can be processed >>> by taking advantage of some of the symmetries in the FFT. I don't >>> recall the details as it has been over a decade since I worked with >>> this, but you can fold half of the real data into the imaginary >>> portion, run a size N/2 FFT and then unfold the results. I believe >>> you have to run a final N sized complex pass on these results to get >>> your final answer. I do recall it saved a *lot* when performing FFTs, >>> nearly 50%. >> >> My understanding is that there were some software packages that baked >> that into the algorithm, for what savings I don't know. I was >> wondering if it was done for FFTs as well. > > I'm not sure what you mean. When you say "baking" it into the > algorithm, it would do pretty much what I described. That *is* the > algorithm. I haven't heard of any other optimizations. The savings is > in time/size. Essentially it does an N/2 size FFT with an extra pass, > so instead of N*log(N) step it takes (N+1)*log(N/2) steps.There's a distinct symmetry to the Fourier transform that you could use at each step of the way instead of doing the whole thing and fixing it up at the end. I don't know if it would save steps, but it would certainly be easier on someone who just wants to apply an algorithm. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com I'm looking for work -- see my website!
Reply by ●February 13, 20172017-02-13
On Sunday, February 12, 2017 at 11:05:25 AM UTC-7, Tim Wescott wrote:> So, there are algorithms out there to perform an FFT on real data, that > save (I think) roughly 2x the calculations of FFTs for complex data. >I could be mistaken, but doesn't the DCT, which is used for video compression, operate only on real data? It seems like you could find a DCT core designed for JPEG.