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32 Bit Floating Point File Format

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  • 32 Bit Floating Point File Format

    Recently, the question arose as to whether Diamond Cut Audio Software would ultimately ever support 32 bit floating point audio data formats. The answer is no and here is why:

    In non-floating point format (fixed - integer) that would represent 192 dB of dynamic range. Referenced to 0 dB SPL and the point of pain in my sound-lab and at 1 kHz, I can not hear anything lower in level than - 70 dB, and my hearing is considered to be very good. Further, no audio system is capable of recording or reproducing that degree of bit depth (resolution).

    So, I doubt that we would ever support such a format as it is of no value, especially when one looks at the physics of the thermal noise floor of op amp input stage transistors (about -80 dB). So, it would not be possible to create such an A/D or D/A capable of producing such a result (unless perhaps cryogenic techniques are used for all of the components in the sound system).

    As Rick pointed out to me, if this is done in 32 Bit Floating point, the dynamic range would actually be 1,500 dB.

    Craig

    ps - anyone claiming to be capable of recording that does not understand the physics or mathematics of such a claim. I would call it "the latest in Marketing Technology" - - - nothing more than that.
    Last edited by Craig Maier; 10-31-2017, 03:52 PM.
    "Who put orange juice in my orange juice?" - - - William Claude Dukenfield

  • #2
    I want to put this 32 bit dynamic range signal into a perspective that one can more easily relate to. I did it in fixed decimal format rather than Floating Point. The reason for that is that the numbers become much too large to relate to otherwise.

    Assume that you have a signal generator connected to a volume control, an audio power amplifier, loudspeaker system and a VU meter.

    1. You set the generator at 1 kHz sine wave and adjust the volume control until the VU meter reads -192 dB (the LSB of a 32 bit fixed decimal system).

    2. You measure the power being delivered by the power amplifier into the loud speaker system at that level and it turns out to be 1 uWatt (1 microwatt) which is one-millionth of a Watt.

    3. Then, you slowly increase the volume control setting until the VU meter reads 0 dB (with the signal generator still set to 1 kHz).

    4. You re-measure the power being delivered by the power amplifier into the loudspeaker system at 0 dB (the MSB of a 32 bit system).

    5. The power being delivered will be 18.447 Trillion Watts which is 18,447 Giga Watts.

    6. The Hope Creek Nuclear power plant here in New Jersey produces 1.0 Giga Watts, so you would need a total of 18,447 of that sort of nuclear power plant to supply power to your audio system.

    7. The sound level would kill you instantaneously, so you would not have to worry about paying the power bill.

    Craig

    ps - the total thermal output of the planet (earth) is 44 Trillion Watts, only 2.4 times the required power for our 32 bit audio system proposal. 32 Bit Floating point format would yield something like 1,500 dB. There is no way to relate to that, but I will take a wild guess that it is up in the range of the calculated value to have created the "Big-Bang". Comments are welcome!
    Last edited by Craig Maier; 10-31-2017, 09:46 AM.
    "Who put orange juice in my orange juice?" - - - William Claude Dukenfield

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    • #3
      Another problem with large digital numbers being converted to analog signals is that the thermal drift from the R2R ladder in the D to A far exceeds the lower bits. Indeed the background noise is why the engineers often calculate the ENOB (effective number of bits) and find that the "real" number is far less than thought.

      Marc

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      • #4
        Hi Marc,

        Indeed, that would be a much more useful specification for audio A/D products. But, we do not set the standards.

        Craig

        ps - I am not sure, but I think that Audio A/Ds no longer use the R2R technique. I believe most use delta-sigma conversion.
        Last edited by Craig Maier; 11-28-2017, 01:30 PM.
        "Who put orange juice in my orange juice?" - - - William Claude Dukenfield

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        • #5
          Craig,

          Yes, most A to D convertors use the delta-sigma over-sampling method rather than "dual slope" or others. The D to A is R2R ladder structure technique still (let me know if I missed a new technology!).

          Marc

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          • #6
            I think that the D / A is the same as an A / D (1 bit). R2R I believe is sometimes still used in some instrument applications, especially in the world of physics where things operate at cryo temperatures. But, I have been away from the hardware aspects of it for around 5 years now, so not sure.
            "Who put orange juice in my orange juice?" - - - William Claude Dukenfield

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