To calculate mu, for the interpolating filter, mu=n/W. "n" is the current NCO register contents "W" is the NCO control word In Gardner's paper he says you can approximate this division, then mu=n*(Ti/Ts) From simulations I have done, W is always around 0.5, which means I can approximate the division and now mu=n*2? Has anyone done this, as I am going to use this in an FPGA and division is always to be avoided if possible. -Jacob
Gardner TED - mu calculation
Started by ●July 29, 2011
Reply by ●July 30, 20112011-07-30
>To calculate mu, for the interpolating filter, mu=n/W. >"n" is the current NCO register contents >"W" is the NCO control word > >In Gardner's paper he says you can approximate this division, then >mu=n*(Ti/Ts) > >From simulations I have done, W is always around 0.5, which means I can >approximate the division and now mu=n*2? Has anyone done this, as I am >going to use this in an FPGA and division is always to be avoided if >possible. > >-Jacob > >I had to read the theory multiple times to understand this concept because it takes time for something to sink in the brain. You would be using 2 samples per symbol and hence getting this value of 0.5 for w which is equal to 1/(samples/symbol) + loop filter output. After acquistion in steady-state and with only a timing phase offset, your w will remain close to 0.5 but during acquistion and in case there is a timing frequency offset between the Tx and Rx, its value will keep on changing although it will linger around 1/(samples/symbol), 0.5 here. Hence, you should not approximate it as above in my opinion because it will defeat the whole purpose of employing timing synchronization itself.
Reply by ●July 30, 20112011-07-30
Hey stupident, I have no idea what kind of rubbish you are talking about. The Gardner TED is just a coarse estimate of the derivative of the energy of the signal wrt timing offset. Everything else are minor technical details of particular realization. jacobfenton wrote:> To calculate mu, for the interpolating filter, mu=n/W. > "n" is the current NCO register contents > "W" is the NCO control word > > In Gardner's paper he says you can approximate this division, then > mu=n*(Ti/Ts) > > From simulations I have done, W is always around 0.5, which means I can > approximate the division and now mu=n*2? Has anyone done this, as I am > going to use this in an FPGA and division is always to be avoided if > possible. > > -Jacob >
Reply by ●July 30, 20112011-07-30
> >Hey stupident, > >I have no idea what kind of rubbish you are talking about. The Gardner >TED is just a coarse estimate of the derivative of the energy of the >signal wrt timing offset. Everything else are minor technical details of >particular realization. > > > >jacobfenton wrote: >> To calculate mu, for the interpolating filter, mu=n/W. >> "n" is the current NCO register contents >> "W" is the NCO control word >> >> In Gardner's paper he says you can approximate this division, then >> mu=n*(Ti/Ts) >> >> From simulations I have done, W is always around 0.5, which means I can >> approximate the division and now mu=n*2? Has anyone done this, as I am >> going to use this in an FPGA and division is always to be avoided if >> possible. >> >> -Jacob >> >I think we should show respect to every person here regardless of his level of knowledge. This is one of the finest fora on the internet where we can ask questions from the giants of communications and signal processing. Such practices will discourage less knowledgable people like me to ask questions. Hope you will think about it. Thanks.
Reply by ●July 30, 20112011-07-30
qasimilyas wrote:>> >> Hey stupident, >> >> I have no idea what kind of rubbish you are talking about. The Gardner >> TED is just a coarse estimate of the derivative of the energy of the >> signal wrt timing offset. Everything else are minor technical details of >> particular realization. >> >> >> >> jacobfenton wrote: >>> To calculate mu, for the interpolating filter, mu=n/W. >>> "n" is the current NCO register contents >>> "W" is the NCO control word >>> >>> In Gardner's paper he says you can approximate this division, then >>> mu=n*(Ti/Ts) >>> >>> From simulations I have done, W is always around 0.5, which means I can >>> approximate the division and now mu=n*2? Has anyone done this, as I am >>> going to use this in an FPGA and division is always to be avoided if >>> possible. >>> >>> -Jacob >>> >> > > I think we should show respect to every person here regardless of his level > of knowledge. This is one of the finest fora on the internet where we can > ask questions from the giants of communications and signal processing. Such > practices will discourage less knowledgable people like me to ask > questions. Hope you will think about it. Thanks.Hey, Vlad was hatched knowing *EVERYTHING* Just ask him :> BUT, if he condescends to answering a question, he's often correct.
Reply by ●July 30, 20112011-07-30
>To calculate mu, for the interpolating filter, mu=n/W. >"n" is the current NCO register contents >"W" is the NCO control word > >In Gardner's paper he says you can approximate this division, then >mu=n*(Ti/Ts) > >From simulations I have done, W is always around 0.5, which means I can >approximate the division and now mu=n*2? Has anyone done this, as I am >going to use this in an FPGA and division is always to be avoided if >possible. > >-Jacob > >In more simple terms and less abusive words: I have done Gardner in FPGA but my memory is too vague now. The algorithm is the error detector in a feedback system. The algorithm works for 2 samples per symbol and you implement it as x1*(x2-x0) i.e. for every three samples you get the difference of two side samples times mid sample. But I think you need to apply that every other sample. It does not matter which but the sense of error inverts. The error is then filtered and used in the feedback system to control clock phase if your clock control is configurable. Or you apply it to your interpolator if it is digital-only timing recovery. The feedback loop should settle at minimum error when clock hits symbols correctly. The error is based on the fact that if timing is perfect then x2 - x0 = 0 due to symmetry. Kadhiem
Reply by ●July 30, 20112011-07-30
I don't give a damn about any netcops regardless of their reasoning or motivation. This place is for leisure and advertizing of the industry professionals. Stupidents and amateurs aren't useful as customers neither it is interesting to have a conversation with them; the only benefit is that their helpless bleating occasionally ignites a good discussion. qasimilyas wrote:>>Hey stupident, >> >>I have no idea what kind of rubbish you are talking about. The Gardner >>TED is just a coarse estimate of the derivative of the energy of the >>signal wrt timing offset. Everything else are minor technical details of >>particular realization. >> >> >> >>jacobfenton wrote: >> >>>To calculate mu, for the interpolating filter, mu=n/W. >>>"n" is the current NCO register contents >>>"W" is the NCO control word >>> >>>In Gardner's paper he says you can approximate this division, then >>>mu=n*(Ti/Ts) >>> >>>From simulations I have done, W is always around 0.5, which means I can >>>approximate the division and now mu=n*2? Has anyone done this, as I am >>>going to use this in an FPGA and division is always to be avoided if >>>possible.> I think we should show respect to every person here regardless of his level > of knowledge. This is one of the finest fora on the internet where we can > ask questions from the giants of communications and signal processing. Such > practices will discourage less knowledgable people like me to ask > questions. Hope you will think about it. Thanks.
Reply by ●July 30, 20112011-07-30
> >Hey stupident, > >I have no idea what kind of rubbish you are talking about. The Gardner >TED is just a coarse estimate of the derivative of the energy of the >signal wrt timing offset. Everything else are minor technical details of >particular realization.Only a stupident would have no idea what he's talking about. A thinking person would probably guess that he's just jumbling Gardner's paper on interpolation with his paper on timing error detection. Steve
Reply by ●August 1, 20112011-08-01
>>To calculate mu, for the interpolating filter, mu=n/W. >>"n" is the current NCO register contents >>"W" is the NCO control word >> >>In Gardner's paper he says you can approximate this division, then >>mu=n*(Ti/Ts) >> >>From simulations I have done, W is always around 0.5, which means I can >>approximate the division and now mu=n*2? Has anyone done this, as I am >>going to use this in an FPGA and division is always to be avoided if >>possible. >> >>-Jacob >> >> > >I had to read the theory multiple times to understand this conceptbecause>it takes time for something to sink in the brain. You would be using 2 >samples per symbol and hence getting this value of 0.5 for w which isequal>to 1/(samples/symbol) + loop filter output. After acquistion in >steady-state and with only a timing phase offset, your w will remainclose>to 0.5 but during acquistion and in case there is a timing frequencyoffset>between the Tx and Rx, its value will keep on changing although it will >linger around 1/(samples/symbol), 0.5 here. Hence, you should not >approximate it as above in my opinion because it will defeat the whole >purpose of employing timing synchronization itself. >I would agree with your assesment, but it's interesting that in his own paper on this (Gardner) he states you can approximate this division, and that the loop filter will suppress any accumulated error. I will keep on investigating this further and let you know how it turns out.
Reply by ●August 1, 20112011-08-01
>> >>Hey stupident, >> >>I have no idea what kind of rubbish you are talking about. The Gardner >>TED is just a coarse estimate of the derivative of the energy of the >>signal wrt timing offset. Everything else are minor technical details of>>particular realization. > >Only a stupident would have no idea what he's talking about. A thinking >person would probably guess that he's just jumbling Gardner's paper on >interpolation with his paper on timing error detection. > >Steve > >Yes, I did misrepresent my title, and I am talking about Gardner's paper on "Interpolation in Digital Modems".
