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Author Topic: 96 kHz ?  (Read 3562 times)

Bob Leonard

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Re: 96 kHz ?
« Reply #60 on: November 13, 2017, 10:01:10 pm »

It sounds like you might have that backwards.



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Peter Morris

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Re: 96 kHz ?
« Reply #61 on: November 14, 2017, 01:11:17 am »

Yep.

By increasing the internal processing bit depth to a 40 bit float, I suspect that one would maintain all the significant digits and create near infinite dynamic range.... arguably the best of both worlds computationally.  Still, performing floating point calculations is more difficult and time intensive.  Today's hardware is fast enough that it no longer matters so I suspect we have seen the end of the integer DSP in digital mixers.

We may have to agree to disagree  :) but as i understand it’s not that simple – the resolution you have at the start is 24 bits, the problem occurs (this is overly simplistic) during your processing if you divide an odd number by 2 for example … 3/2 = 1 ½  but you can’t have a ½ in the digital world so you have to round it to 1 or 2 and in doing so you have loss an tiny bit of information.

Sure a 32 bit signal path with an 8 bit exponent (40 bit) gives you huge dynamic range, but it’s not dynamic range that’s the issue (unless you run out of it during your calculations), its accuracy and the less of these rounding errors the better. As I understand fixed point can produce less of these types of errors if done correctly.

This is what Patrick Warrington, Calrec Technical Director said in his paper - "DISPELLING THE MYTH OF THE FLOATING-POINT" that I posted earlier.

(Calrec make very serious Broadcast Consoles https://calrec.com/ they are part of the Audiotonix group which includes Digico, Calrec, Allen & Heath and DigiGrid  http://audiotonix.com/ )

“It is an inescapable consequence of the format that as floating-point numbers whiz around the numerical firmament, they deposit little piles of arithmetic ejectamentain their wake. In the interest of balance, I would point out that the errors are, on the whole, quite small, and that for the majority of calculations, they are irrelevant, especially when compared to the more serious threats to quality along the route from microphone to living room. But if we choose to make numerical precision an aim (which we should) then we ought to do it properly and not let the want of a little analysis be a barrier to good science.”

i.e. done correctly there is a very small sound accuracy / quality advantage with fixed point, and similarly with 96kHz. With respect to the 96kHz its mostly about the being able to using anti-alias filters with lower slopes. This results in less phase distortion and smearing in the VHF, giving you a better a stereo image and being less fatiguing to listen to … but we are talking about very tiny differences.

This combination is also very fast and contributes to achieving very low latency - a must for some IEM applications.
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Scott Holtzman

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Re: 96 kHz ?
« Reply #62 on: November 14, 2017, 03:10:11 am »

Floating point has no more resolution than integer based when you are talking equal bit depths.  Most modern consoles use 24-bit, bit depths which gives 16,777,216 points of resolution within a single value.  This is true regardless of whether or not you are using floating point representation or integer values.

Scott, I don't understand what you are trying to say.  You can represent the number of unique values is not the point of bit depth.  Bid depth is dynamic range and sample rate drives frequency response. 

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Frank Koenig

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Re: 96 kHz ?
« Reply #63 on: November 14, 2017, 01:27:09 pm »

There's always "bignums" AKA Arbitrary-Precision Arithmetic. It's an integer numeric format that expands as needed limited only by available storage. Fun stuff, but admittedly not very relevant to ordinary signal processing.   :o  -F
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Corey Scogin

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Re: 96 kHz ?
« Reply #64 on: November 14, 2017, 04:57:03 pm »

We may have to agree to disagree  :) but as i understand it’s not that simple – the resolution you have at the start is 24 bits, the problem occurs (this is overly simplistic) during your processing if you divide an odd number by 2 for example … 3/2 = 1 ½  but you can’t have a ½ in the digital world so you have to round it to 1 or 2 and in doing so you have loss an tiny bit of information.

Sure a 32 bit signal path with an 8 bit exponent (40 bit) gives you huge dynamic range, but it’s not dynamic range that’s the issue (unless you run out of it during your calculations), its accuracy and the less of these rounding errors the better. As I understand fixed point can produce less of these types of errors if done correctly.

This is what Patrick Warrington, Calrec Technical Director said in his paper - "DISPELLING THE MYTH OF THE FLOATING-POINT" that I posted earlier.
“It is an inescapable consequence of the format that as floating-point numbers whiz around the numerical firmament, they deposit little piles of arithmetic ejectamentain their wake. In the interest of balance, I would point out that the errors are, on the whole, quite small, and that for the majority of calculations, they are irrelevant, especially when compared to the more serious threats to quality along the route from microphone to living room. But if we choose to make numerical precision an aim (which we should) then we ought to do it properly and not let the want of a little analysis be a barrier to good science.”

I just read through all 3 of the articles you listed here…

https://calrec.com/wp-content/themes/calrec/pdf/Myth-of-the-Floating-Point.pdf
http://www.jamminpower.com/PDF/48-bit%20Audio.pdf
http://www.rane.com/pdf/old/note153.pdf

And realized that in each of these articles, they're discussing actual DSP implementations of floating point vs fixed and how the referenced DSP chips can "scale" fixed point using double precision when necessary whereas the floating point chips do not. So, they're saying that doubling the register size in fixed point is better than just using floating point’s built-in scaling.

In a way, this is comparing apples to oranges academically, but apples to apples practically.

My thoughts here were correct then:

What if we think about it in terms of significant digits. If A/D is 24-bit fixed and internal processing is 32-bit float (for example) with a 24 bit mantissa and an 8 bit exponent (ignoring the sign bit for this example), we still have 24 “significant bits”, never more, never less.

The Rane article does a better job of explaining this in an example of 32-bit float vs 24-bit double-precision (48-bit) capable DSPs.

What is required in a floating-point DSP to achieve superior
audio? Here are some pretty nasty “ifs” necessary for floating-point
to overtake fixed-point: if it is a 56-bit floating-point
processor (i.e., 48-bit mantissa plus 8-bit exponent) or 32-bit
with double-precision (requiring a large accumulator), if the
parts run at the same speed as the equivalent fixed-point part,
if they use the same power, and if they cost the same, then the
choice is made.

So my conclusion is this: Yes, floating point is better than fixed point given the float’s mantissa is the same bit width as the fixed point.
However, in practice, fixed point DSPs require less speed and power to achieve the same results by doubling the register width (bit width) used during calculations that need it. Apparently, floating-point DSPs can't as easily scale the bit width as easily.

For the end user of mixing consoles: As long as the console designers have been careful in their DSP design, neither inherently produces better audio quality.
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Scott Bolt

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Re: 96 kHz ?
« Reply #65 on: November 14, 2017, 06:58:51 pm »

Corey,

I agree.

I believe it is easier to write good floating point routines than it is good integer routines (I have done both).  The big difference I have found is the computational work load is much higher for FP.

If the hardware can easily handle the work load, then FP will generally result in better routines since the programmer can spend more time making the routine do what they want it to do, and less time worrying about losing resolution by hitting the ceiling or floor.

As for the previous example of dividing an odd number by 2 .....

If you use an integer of 3 (represented as 0000 0000 0000 0011b) and divide it by 2 in integer math you get 1 (shifting the bits right is the same as dividing by 2).

If you do the same exercise in floating point, using the same number of bits, you get 1.5.

In integer math, the way that you typically avoid this problem is that you first multiply by a big number (and a power of 2 so you can use shift left which is very fast) prior to the divide.  Of course, the shifting of bits to the left loses significance for big numbers.

As you can see, integer math is very tricky if you want to remain accurate and not lose significance.

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Peter Morris

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Re: 96 kHz ?
« Reply #66 on: November 15, 2017, 05:26:35 am »

Scott and Corey,

I agree with what you have said … and my 3 divided by 2 as I said was overly simplistic – for the reason Scott noted but I was just to try to find a simple way to explain how rounding errors can affect things. Both the Rane and Calrec’s papers have much better examples but they are complicated to explain at lounge level.

Cory quoted this from the Rane article:

“What is required in a floating-point DSP to achieve superior audio? Here are some pretty nasty “ifs” necessary for floating-point to overtake fixed-point: if it is a 56-bit floating-point processor (i.e., 48-bit mantissa plus 8-bit exponent) or 32-bit with double-precision (requiring a large accumulator), if the parts run at the same speed as the equivalent fixed-point part, if they use the same power, and if they cost the same, then the choice is made”

What I have been talking about is more or less 40 bit floating point Vs fixed point with a stupid and variable bit depth, more like 72 bit with a 96 bit accumulator and I have ignored cost. In practical terms the sound quality of my Midas Pro 2 Vs my dLive.

In the Rane acritical they noted -
 
“Floating-point evangelists like to use an example where the processor is set up for 60 dB attenuation on the input and 60 dB make-up gain on the output. Leaving aside the absurdity of this fabricated example, let’s use it to make our fixed-point-is-better point: add a second input to this example, with the gain set for unity, a 0 dBu signal coming in, and configure the processor to sum both these channels into the output and listen to the results — you will not like what you hear.”

In other words it depends on exactly what you are doing as to what attributes are the most important … we don’t do 60 dB of attenuation followed by 60dB of gain but we do add big and very small signals (floating point are not good at this).

The article then goes on to say –

“ Another revealing example is how you never hear floating point advocates talk about low-frequency/high-Q filter behavior. The next time you get the opportunity, set up a floating-point box parametric filter for use as a notch filter with a center frequency of 50 Hz and a Q of 20. First listen to the increase in output noise. Now run an input sweep from 20 Hz to 100 Hz and listen to all the unappetizing sounds that result. Audio filters below about 100 Hz require simultaneous processing of large numbers and small numbers — something fixed-point DSPs do much better than their floating-point cousins”

This example is also given in the Calrec paper and includes some measurements & graphs, but we tend not to do that many high Q notch LF filters, but there are some issues with LF EQ biquad implementations.
 
There are advantages and disadvantages to both approaches but it depends on what mathematical compromises have been taken as to what the resulting sound quality will be.  Its really matters of finding the best overall compromise, latency, sound quality, cost, number of busses etc. On the matter of busses our Pro2 cannot do pre fadder, pre EQ Aux sends because of the limitations in the DSP architecture.

Calrec have implemented their fixed point mathematics using their “Bluefin2 DSP” technology. It uses a variable bit depth and I suspect the A&H being part of the same group have implement similar technology in the dLive which also has a variable bit depth.

The proof is of course - the resulting sound quality. I am aware that at least one company in the UK has done some extensive testing of various consoles measuring THD, noise floors etc. and found that the dLive was the best sounding console they have! My ears are telling the same.
 
What I love about this discussion is that it is highlighting some of the major things that contribute to the sound of a desk; it’s not just the pre-amps (so over that statement)! To appreciate / test the quality you must be doing a mix, summing inputs and adding EQ, compression, gates etc … listening to an MP3 file through two channels with no EQ will not tell you very much at all.
« Last Edit: November 15, 2017, 05:28:49 am by Peter Morris »
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Scott Slater

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Re: 96 kHz ?
« Reply #67 on: November 15, 2017, 05:59:30 am »

This statement is untrue.

The resolution of the floating point value depends on the mantissa or "value" part of the number. It requires more bits to implement the exponent. Ex: 32-bit float with a 24-bit mantissa and 8 bit exponent is equal in resolution to 24-bit fixed.

Most consoles use 24-bit A/D and D/A but internal processing is higher. The X32 is 40-bit float internally.

That's not what I said.  If you are comparing 32 total bits (24+8 as per your example) to 24 total bits, then yes, 32 has more overall resolution.  But if you have only 32 or 24 bits total in which to store (or transport) digital information, then they have the exact same number of possibilities with those specific SET amount of bits.  As I said a 24-bit value only has 16.7M possible combinations.  What values are represented by those bits are irrelevant.
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Scott Slater

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Re: 96 kHz ?
« Reply #68 on: November 15, 2017, 06:08:54 am »

Scott, I don't understand what you are trying to say.  You can represent the number of unique values is not the point of bit depth.  Bid depth is dynamic range and sample rate drives frequency response.

Exactly.  Bit depth basically like a Y-axis and sampling rate an X-axis.  I was talking about the number of representations with a single 24-bit sample are the same no matter what value is represented by the sample (floating or integer).  Min could be 0 while Max could represent 1, and everything in between could be floating point values between zero and one, or they could be whole numbers from 0 to 16,777,215.  Either way there are exactly the same number of possibilities given a set number of bits.

Also I understand that processing bits, and algos have nothing to do with transport/storage bits algos.  I'm simply saying that a single PCM audio sample will always be limited to amplitude by the number of bits per sample used, and frequency by the number of samples per second used.
« Last Edit: November 15, 2017, 07:03:24 am by Scott Slater »
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Roland Clarke

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Re: 96 kHz ?
« Reply #69 on: November 15, 2017, 06:39:53 pm »

I think of 96 kHz in sound as being similar to a higher mega-pixel (MP) count in photography (my day job): more usable information if your output can make use of it. A 4x6 at the corner drugstore can only use so many pixels to make the photograph while a 30" x 40" print from a pro lab will use, and show, everything that was captured initially. Along with high MP files comes the need for more processing power in the computer doing the image processing. I assume that a 96 kHz capture device (newish board) would have significantly more on-board processing power than and older 44/48 kHz-capable board would.

Could the more powerful chipset be the reason for the lower latency with a 96 kHz board?

Not really.  The lower latency on higher frequency samplerates is usually a function of buffer size on the AD/DA,  basically twice the data of 48khz, half the buffer fill up time.
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