Sur la pd-list, Cyrille Henry et Miller Puckette nours parlent de la résolution (plage dynamique) de l'oreille humaine,


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 < <>>: Nice. Thanks Chuck, I learnt something. On 22 April 2015 at 23:45, Charles Z Henry < <>> wrote: On Wed, Apr 22, 2015 at 5:11 PM, Alexandre Torres Porres < <>> 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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