On Thu, 21 Mar 2013 21:38:39 -0500, the renowned Jamie <jamie_ka1lpa_not_valid_after_ka1lpa_@charter.net> wrote: .> > Many of these DDS FG's seem to show that anything other than a sine >wave, forces them to reduce output BW. I can only assume this due to a >bottle neck from the uC to the chip to update pattern configuration via >SPI or C2I.. I guess a parallel version would make a vast improvement. > >JamieCompare the bandwidth of a sine wave of frequency f vs. a sawtooth of the same frequency. Best regards, Spehro Pefhany -- "it's the network..." "The Journey is the reward" speff@interlog.com Info for manufacturers: http://www.trexon.com Embedded software/hardware/analog Info for designers: http://www.speff.com
Sine Lookup Table with Linear Interpolation
Started by ●March 16, 2013
Reply by ●March 21, 20132013-03-21
Reply by ●March 22, 20132013-03-22
On 17/03/2013 22:57, John Larkin wrote:> On Sun, 17 Mar 2013 18:44:07 -0400, rickman <gnuarm@gmail.com> wrote: > >> On 3/17/2013 6:20 PM, John Larkin wrote: >>> >>> It would be interesting to distort the table entries to minimize THD. The >>> problem there is how to measure very low THD to close the loop. >> >> It could also be a difficult problem to solve without some sort of >> exhaustive search. Each point you fudge affects two curve segments and >> each curve segment is affected by two points. So there is some degree >> of interaction. >> >> Anyone know if there is a method to solve such a problem easily? I am >> sure that my current approach gets each segment end point to within �1 >> lsb and I suppose once you measure THD in some way it would not be an >> excessive amount of work to tune the 256 end points in a few passes >> through. This sounds like a tree search with pruning. > > If I could measure the THD accurately, I'd just blast in a corrective harmonic > adder to the table for each of the harmonics. That could be scientific or just > iterative. For the 2nd harmonic, for example, add a 2nd harmonic sine component > into all the table points, many of which wouldn't even change by an LSB, to null > out the observed distortion. Gain and phase, of course. > >> >> I'm assuming there would be no practical closed form solution. But >> couldn't the THD be calculated in a simulation rather than having to be >> measured on the bench? > > Our experience is that the output amplifiers, after the DAC and lowpass filter, > are the nasty guys for distortion, at least in the 10s of MHz. Lots of > commercial RF generators have amazing 2nd harmonic specs, like -20 dBc. A table > correction would unfortunately be amplitude dependent, so it gets messy fast.Is it really "pure" second harmonic distortion or a tiny mismatch in the gain bandwidth product of the power amplifier that could be tweaked out by a small change in the digital amplitude of the negative cycle? -- Regards, Martin Brown
Reply by ●March 22, 20132013-03-22
On 3/18/2013 7:18 PM, glen herrmannsfeldt wrote:> In comp.dsp rickman <gnuarm@gmail.com> wrote: >> On 3/18/2013 2:10 PM, Jerry Avins wrote: > > (snip, ending on CORDIC) > >>> http://www.andraka.com/files/crdcsrvy.pdf should be a good start. Do you >>> remember Ray Andraka? > >> Yes, of course. I should have thought of that. I don't go to his site >> often, but his stuff is always excellent. I may have even downloaded >> this paper before. I took a look at the CORDIC once a few years ago and >> didn't get too far. I'm happy with my current approach for the moment, >> but I will dig into this more another time. > > I once thought I pretty well understood binary CORDIC, but it > is also used in decimal on many pocket calculators. I never got > far enough to figure out how they did that.The hp35 used CORDIC to compute trig functions. Its basic math operations were BDC, using decimal arithmetic. Most CORDIC implementations skip "irrelevant" rotations, so the scale of the result isn't constant for all inputs. To get sine, the hp35 computed both sine and cosine (little extra cost for getting both) which had the same scale, then divided to get the cotangent-- the scale factors cancel. 1/sqrt(cot(x)^2 + 1) = sin(x). Since the arithmetic functions were all in place, it was the fastest way to the result. So what does "simple" really mean? Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●March 22, 20132013-03-22
In comp.dsp Jerry Avins <jya@ieee.org> wrote: (snip, I wrote)>> (snip, ending on CORDIC)(snip)>> I once thought I pretty well understood binary CORDIC, but it >> is also used in decimal on many pocket calculators. I never got >> far enough to figure out how they did that.> The hp35 used CORDIC to compute trig functions. Its basic math > operations were BDC, using decimal arithmetic. Most CORDIC > implementations skip "irrelevant" rotations, so the scale of the result > isn't constant for all inputs.The usual binary explanation is that you rotate one way or the other, such that the scale is constant. Then multiply (once) to correct for that scale, or for any other scale you want the result to have.> To get sine, the hp35 computed both sine > and cosine (little extra cost for getting both) which had the same > scale, then divided to get the cotangent-- the scale factors cancel. > 1/sqrt(cot(x)^2 + 1) = sin(x). Since the arithmetic functions were all > in place, it was the fastest way to the result.Does sound better than convert to binary followed by binary CORDIC. If you really aren't in a hurry, you can do 0 to 9 rotations for each digit.> So what does "simple" really mean?Sometimes it means no divide and few mutliplies. I think I have previously noted the Integer Cosine Transform for when you need to do something like FFT, but with minimal multiplies. (And when you have lots of processing power for the inverse.) Designed for the CDP1802, which doesn't have a multiply. Integer cosine site:jpl.nasa.gov into google should find it. -- glen
Reply by ●March 22, 20132013-03-22
Jerry Avins wrote:> On 3/18/2013 7:18 PM, glen herrmannsfeldt wrote: >> In comp.dsp rickman <gnuarm@gmail.com> wrote: >>> On 3/18/2013 2:10 PM, Jerry Avins wrote: >> >> (snip, ending on CORDIC) >> >>>> http://www.andraka.com/files/crdcsrvy.pdf should be a good start. Do >>>> you >>>> remember Ray Andraka? >> >>> Yes, of course. I should have thought of that. I don't go to his site >>> often, but his stuff is always excellent. I may have even downloaded >>> this paper before. I took a look at the CORDIC once a few years ago and >>> didn't get too far. I'm happy with my current approach for the moment, >>> but I will dig into this more another time. >> >> I once thought I pretty well understood binary CORDIC, but it >> is also used in decimal on many pocket calculators. I never got >> far enough to figure out how they did that. > > The hp35 used CORDIC to compute trig functions. Its basic math > operations were BDC, using decimal arithmetic. Most CORDIC > implementations skip "irrelevant" rotations, so the scale of the result > isn't constant for all inputs. To get sine, the hp35 computed both sine > and cosine (little extra cost for getting both) which had the same > scale, then divided to get the cotangent-- the scale factors cancel. > 1/sqrt(cot(x)^2 + 1) = sin(x). Since the arithmetic functions were all > in place, it was the fastest way to the result. > > So what does "simple" really mean? > > JerrySomeone pointed out that i quoted sqrt(50) incorrectly at 6 digits; the actual table in CRC shows 7.071068 which is seven digits, definitely better than the puny 4 digits that was bandied about.
Reply by ●March 22, 20132013-03-22
Spehro Pefhany wrote:> On Thu, 21 Mar 2013 21:38:39 -0500, the renowned Jamie > <jamie_ka1lpa_not_valid_after_ka1lpa_@charter.net> wrote: > > . > >> Many of these DDS FG's seem to show that anything other than a sine >>wave, forces them to reduce output BW. I can only assume this due to a >>bottle neck from the uC to the chip to update pattern configuration via >>SPI or C2I.. I guess a parallel version would make a vast improvement. >> >>Jamie > > > Compare the bandwidth of a sine wave of frequency f vs. a sawtooth of > the same frequency. > > > Best regards, > Spehro PefhanySomething tells me that not all DDS chips are created equal. Jamie
Reply by ●March 23, 20132013-03-23
On Thu, 21 Mar 2013 17:51:42 -0400, rickman <gnuarm@gmail.com> wrote:> >>>>>> if you assume an approximate quadratic behavior over that short segment, >>>>>> you can compute the straight line where the error in the middle is equal >>>>>> in magnitude (and opposite in sign) to the error at the end points. >>>>>> that's a closed form solution, i think. >>>>> >>>>> Yes, it is a little tricky because at this point we are working with >>>>> integer math (or technically fixed point I suppose). >>>> >> >> Hmm. I would like to take a crack at simpson's rule interpolation for >> this to measure error budget. I may not be timely but this is >> interesting. joseph underscore barrett at sbcglobal daht cahm > >Oh, I thought you were talking about using Simpsom's rule as part of the >interpolation. You are talking about using it to estimate the integral >of the error. Great idea! I'll shoot you an email.I was talking about using it for interpolation. ?-)
Reply by ●March 23, 20132013-03-23
On 3/23/2013 2:42 PM, josephkk wrote:> On Thu, 21 Mar 2013 17:51:42 -0400, rickman<gnuarm@gmail.com> wrote: > >> >>>>>>> if you assume an approximate quadratic behavior over that short segment, >>>>>>> you can compute the straight line where the error in the middle is equal >>>>>>> in magnitude (and opposite in sign) to the error at the end points. >>>>>>> that's a closed form solution, i think. >>>>>> >>>>>> Yes, it is a little tricky because at this point we are working with >>>>>> integer math (or technically fixed point I suppose). >>>>> >>> >>> Hmm. I would like to take a crack at simpson's rule interpolation for >>> this to measure error budget. I may not be timely but this is >>> interesting. joseph underscore barrett at sbcglobal daht cahm >> >> Oh, I thought you were talking about using Simpsom's rule as part of the >> interpolation. You are talking about using it to estimate the integral >> of the error. Great idea! I'll shoot you an email. > > I was talking about using it for interpolation.The email bounced. -- Rick
Reply by ●March 23, 20132013-03-23
On Thu, 21 Mar 2013 18:45:15 -0700, John Larkin <jlarkin@highlandtechnology.com> wrote:>On Thu, 21 Mar 2013 18:45:02 -0400, rickman <gnuarm@gmail.com> wrote: > >>On 3/21/2013 1:14 PM, John Larkin wrote: >>> On Wed, 20 Mar 2013 20:53:13 -0700, josephkk >>> <joseph_barrett@sbcglobal.net> wrote: >>> >>>> On Sun, 17 Mar 2013 17:22:59 -0700, John Larkin >>>> <jjlarkin@highNOTlandTHIStechnologyPART.com> wrote: >>>> >>>>> >>>>>> I don't think you are clear on this. The table and linear interp are as >>>>>> good as they can get with the exception of one or possibly two lsbs to >>>>>> minimize the error in the linear interp. These is no way to correct for >>>>>> this by adding a second harmonic, etc. Remember, this is not a pure >>>>>> table lookup, it is a two step approach. >>>>> >>>>> Why can't some harmonic component be added to the table points to improve >>>>> downstream distortion? Of course, you'd need a full 360 degree table, not a >>>>> folded one. >>>> >>>> How do you get that? All harmonics would be within the 90 degree table. >>> >>> Second? >> >>Actually this would not work for anything except odd harmonics. The way >>the table is folded they have to be symmetrical about the 90 degree >>point as well as the X axis at 0 and 90 degrees. Odd harmonics would do >>this if they are phased correctly. I don't think it would be too useful >>that way. > >Just looking at a sine at F and one at 2F, it's obvious that the 90 >degree folded table can't make the 2F component. The 2nd harmonic has >to change sign between 0-90 degrees and 90-180 but can't if the same >90 degree table is used. > >> >> >>>> Harmonic phase shifts is a different matter though, that would take >>>> careful characterization of production quantities of the final product, >>>> $$$$$. >>> >>> Of course you'd have to null each harmonic for gain and phase, >>> preferably on each production unit, but it wouldn't be difficult or >>> expensive *if* you had a distortion analyzer with the required PPM >>> performance. We regularly do automated calibrations, polynomial curve >>> fits and such, more complex than this. >> >>Might as well use a separate table for the nulling, it would be much >>simpler. > >It's really about the same, but I guess if the main table is heavily >interpolated, it would make sense to have a little distortion table >off to the side, maybe even with its own DAC.The table is always valid. The only difference in frequency is the phase accumulator stepping rate. That is why a DDS is "tunable". ?-)
Reply by ●March 24, 20132013-03-24
On Wed, 20 Mar 2013 19:25:02 -0400, rickman <gnuarm@gmail.com> wrote:>On 3/20/2013 7:05 PM, josephkk wrote: >> >> Without reading any other replies, i would suggest either the CORDIC >> algorithm of simpson's rule interpolation. From the rule for integration >> to find any intermediate value you evaluate the curve value within the >> segment covered by rule. 4 intervals on the step size you have will be >> limited by the 18 bits of input. Do 20 bits of input and round to 18 or >> not. About 1 PPM. > >I can't say I follow what you mean about Simpson's rule interpolation. >Interpolation is used to derive Simpson's Rule, but I don't see a way to >use an integral for obtaining an interpolation. Isn't Simpson's Rule >about approximating integrals? What am I missing?In many ways it is just an estimator with somewhat less than second order complexity for function sections of greater than second order complexity. It is useful in integration because it reduces error and complexity for reasonably smooth functions. Its value for interpolating within a segment comes from there. ?-)
