[PD] audio bit resolution in Pd

[Cyrille Henry]

Le 23/04/2015 17:25, Miller Puckette a écrit :
> I get 1 000 000 = 2^19.9 so a 20 bit dynamic range.
yes, your right,
thanks for the correction
c

>
> I don't think A/D/A hardware ever gets better than about 110 dB dtnamic
> range though.
>
> cheers
> Miller
>
> On Thu, Apr 23, 2015 at 05:20:51PM +0200, Cyrille Henry wrote:
>>
>>
>> Le 23/04/2015 16:41, Alexandre Torres Porres a écrit :
>>> Yep, nice indeed, I guess I learned - in short and in layman's undetailed terms - that audio output is ~24bits (a bit higher, but much higher for smaller numbers).
>>>
>>> Moreover, digital audio cards won't likely have more than 24 bit precision for many years to come, so it's just way more than enough.
>> The human ear is usually consider to be sensible from 0dB to 120dB, so a range of 10^(12/2) between the smallest and biggest amplitude.
>> i.e from 1 to 1 000 000, or from 1 to 2^13.8
>> so, the human ear sensitivity can be considered to be about 14 bits.
>> 16 bits diffusion should be enough.
>> 24 bits diffusion is already overkill.
>>
>> cheers
>> c
>>
>>>
>>> thanks
>>>
>>>
>>> 2015-04-23 6:43 GMT-03:00 Julian Brooks <jbeezez at gmail.com <mailto:jbeezez at gmail.com>>:
>>>
>>>     Nice. Thanks Chuck, I learnt something.
>>>
>>>     On 22 April 2015 at 23:45, Charles Z Henry <czhenry at gmail.com <mailto:czhenry at gmail.com>> wrote:
>>>
>>>         On Wed, Apr 22, 2015 at 5:11 PM, Alexandre Torres Porres
>>>         <porres at gmail.com <mailto:porres at gmail.com>> wrote:
>>>
>>>         > So I start with this idea that the audio (values from -1 to 1) can't be in
>>>         > full 32 bit float resolution, it's less. I don't see why that is "wrong".
>>>         > And then, from it, my first question here was: "what is the audio resolution
>>>         > then?". I'm still clueless here about this answer.
>>>         >
>>>         > Moreover, is it more or less than what 24 bit audio cards handle?
>>>
>>>         Let me try:
>>>
>>>         32-bit floating point numbers have 24 bits of precision.  Always.  The
>>>         remaining 8 bits are just for the sign and exponent.  When the
>>>         amplitude of the signals decrease, you don't lose any precision in
>>>         floating-point.  The value of the least significant bit (LSB) gets
>>>         proportionally smaller.
>>>
>>>         However, the output of a 24-bit soundcard always has a fixed
>>>         quantization.  The LSB is always the same size.  Smaller numbers have
>>>         less precision.
>>>
>>>         The mismatch occurs when converting from the 32-bit floats to the
>>>         24-bit fixed point numbers.  Now, the smaller numbers aren't as
>>>         precise anymore.  They get rounded to the nearest number in the 24-bit
>>>         fixed point system.
>>>
>>>         So, yes, the resolution (of small numbers) in floating point (internal
>>>         to Pd) is finer than the resolution of those numbers when output
>>>         (driver/DAC).
>>>
>>>         Also, the 24-bit fixed point format is for values between -1 and 1.
>>>         That means that numbers between 0 and 1 have just 23 bits.  In 32-bit
>>>         math, the numbers between 0.5 and 1 still have 24 bits of precision
>>>         (the sign is held elsewhere).  That means that Pd's internal
>>>         resolution is finer than the soundcard resolution for all numbers
>>>         between -1 and 1.
>>>
>>>         Chuck
>>>
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