[PD] audio bit resolution in Pd

[Miller Puckette]

I get 1 000 000 = 2^19.9 so a 20 bit dynamic range.

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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