# [PD] audio bit resolution in Pd

Cyrille Henry ch at chnry.net
Thu Apr 23 17:20:51 CEST 2015

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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
>         >
>         > 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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