[endless402]

Phase question:

My amplifier has the following XLR inputs for phase:
Balanced input connectors: Pin 2 is negative, Pin 3 is positive (I could flip these with a phase switch)

On the chord dave, which phase setting would be correct?

 

[Apos001]

It gets on my nerves as well. This is just Shannon's sampling theorem - nothing mystical.

If you want to see something actually 'mystical' check this out (watch out like Shannon's Sampling Theorem math required).

There is this mathematical function, the so called zeta function which is ζ(s) = 1/1^s + 1/2^s + 1/3^s ......... Now put in k = 0, -1, - 2 etc and you get for k=0 1+1+1+1......, or k=-1 1 +2 + 3 etc. These look like infinity. But not so fast attendant reader - lets actually calculate it for all values -k.

∑(-1)^k*ζ(-k)*x^k/k! = ∑∑ n^k*(-x)^k/k! = ∑ ∑(-nx)^k/k! = ∑e^(-nx). Let S = ∑e^(-nx). e^xS = 1 + S so S = 1/e^x - 1 = 1/x*x/e^x - 1. But one of the definitions of the so called Bernoulli numbers Bk, is x/(e^x - 1) = ∑Bk*x^k/k! or taking the1/x into the sum S = ∑ B(k+1)*x^k/(k+1)! after changing the summation index so you still have powers of x^k. Thus you have ∑(-1)^k*ζ(-k)*x^k/k! = ∑ B(k+1)*x^k/(k+1)!. Equating the coefficients of the power of x^k you have ζ(-k) = (-1)^k*B(k+1)/k+1.

This result implies the bizarre identities ζ(0) = 1+1+1+1....... = -1/2 and ζ(1) = 1+2+3+4....... = -1/12.

Now that's magic - not like Shannon's sampling theorem that is simple basic engineering math. The why of the above is much more complicated - but unsuitable for here. You can do a bit of internet research on that one or go to a science forum and ask someone - I personally use Physics Forums. I will have to tell you though only some people actually understand it (technically it's got to do with complex analysis and avoiding the pole at s = 1 that causes the infinity - but that is likely meaningless unless you know complex analysis). You will hear all sorts of views like such sums are just definitions etc. In fact its used in calculations of real physical problems like the so called Casmir Force so is not just a definition - it has real physical consequences.

This is just to point out you cant really discuss this stuff, including what Rob does, without REALLY knowing the math behind it. English is a very poor medium for doing that. Rob has explained it many times - its simple math and the consequences irrefutable, but some just do not get it.

Thanks
Bill

The analytic continuation of ζ(.) function has that property ( ζ(1)=-1/12, ζ(0)=-1/2 ), not the above series. The flaw in your proof is that you are doing calculations with series that do not converge. You cannot do calculations with divergent series, simply those calculations are not defined.

"The above series is a prototypical Dirichlet series that converges absolutely to an analytic function for s such that σ > 1 and diverges for all other values of s. " from:

https://en.wikipedia.org/wiki/Riemann_zeta_function#:~:text=The Riemann zeta function is,function defined for σ > 1.&text=Thus the Riemann zeta function,s = 1 with residue 1.

The analytic continuation is totally another function.

Definitely 1+2+3+... = inf

The thing you are referring to is just notation. We do write 1+2+3+... = -1/12, but we mean that the analytic continuation converges there, and obviously not the limit of the finite sums of (n).

Regards,
Apostolos

 

[Rob Watts]

Phase question:

My amplifier has the following XLR inputs for phase:
Balanced input connectors: Pin 2 is negative, Pin 3 is positive (I could flip these with a phase switch)

On the chord dave, which phase setting would be correct?

So Dave is pin 2 positive, pin 3 negative. So set Dave to Neg phase (assuming your power amp does not invert too!).

Happy listening Rob

 

[gasmonkey]

Hi Rob. I remember one time you weren't so optimistic of the future of FPGA's, in the context of above and beyond 1 million taps, through to 256 million taps, in the near future. I don't have the exact quote on me

I'm reading through The $37 Arrow DECA FPGA Board and they kinda trash a FPGA, ("A Max10 FPGA can run a VexRiscv soft core at ~100MHz, which is a far cry of the 240MHz that’s reported for the already dated and not terribly fast Artix-7.") The Artix-7, I'm thinking to myself, I know that thing! So I google it, and that's the chip!

I'm looking at whats new from Xilinx, and they have this, an upgrade to the Artix line: Artix UltraScale+ FPGA Family.

How does that stack up, and does it excite you in any way? What are your thoughts on the current state of FPGA's? If you got to control the finances for the R&D department of Xilinx, what direction would you push FPGA's in so you could use them to accomplish your audio dreams?

 

[Rob Watts]

Yes when I saw that announcement last month (I was just starting my 10km morning hike) I got very excited with the possibilities of 1200 dsp cores and much lower power. But when I got back and downloaded the data sheets, I was in for a disappointment; it may have 1200 cores, but has very slightly less memory than the 200T (the M scaler FPGA). So it will be memory limited. Also, given Xilinx track record, and the current severe problems with supply from silicon, it will be unobtainable for several (perhaps many) years. And probably expensive...

So my needs are simple and probably similar to others - more on chip memory, more dsp cores, more fabric, and much lower power - and lower cost! All of which together is not looking possible or probable.

 

[hmartin]

Yes when I saw that announcement last month (I was just starting my 10km morning hike) I got very excited with the possibilities of 1200 dsp cores and much lower power. But when I got back and downloaded the data sheets, I was in for a disappointment; it may have 1200 cores, but has very slightly less memory than the 200T (the M scaler FPGA). So it will be memory limited. Also, given Xilinx track record, and the current severe problems with supply from silicon, it will be unobtainable for several (perhaps many) years. And probably expensive...

So my needs are simple and probably similar to others - more on chip memory, more dsp cores, more fabric, and much lower power - and lower cost! All of which together is not looking possible or probable.

I guess the memory need depend on how the processing power is spent. For example, going to a 32x FIR msc i.e.1536 kHz instead of 768 kHz upsampling would be an option. But this would imply an new interface e.g. Optical or integrating the 32x msc in the same box as the DAC?

 

[The Jester]

Maybe keeping them apart more needed with increased clock speeds ?
dual boxes with a proprietary fibre optic cable as Toslink is limited by the transponders ?
onboard lithium batteries and magnetic charging technology for ultimate isolation ...
would it be feasible to use 2 smaller FPGA’s in parallel ?

 

[IgeNeLL]

My combination

 

[audionewbi]

@IgeNeLL What IEM are those?

 

[Ronengeller]

Hi Rob, had you had a need to use an IEM, which one would it be, in terms of sound only, that does most of the things right?

 

[ZappaMan]

Hi Rob, had you had a need to use an IEM, which one would it be, in terms of sound only, that does most of the things right?

Robs ears are far too hairy to fit Iems in. It would be more appropriate to plant potatoes in robs ears.

 

[jlbrach]

huh?

 

[Kentajalli]

Robs ears are far too hairy to fit Iems in. It would be more appropriate to plant potatoes in robs ears.

mind boggles as to how you know how much hair he's got and where!

 

[ZappaMan]

huh?

Horticultural patch

 

[Rob Watts]

Hi Rob, had you had a need to use an IEM, which one would it be, in terms of sound only, that does most of the things right?

I don't get on with IEMs. I had a couple of custom units, and after an hour my ears ache. I did like Noble Kaiser IEMs though, but I haven't tried everything available today.