[PD] audio bit resolution in Pd

Julian Brooks jbeezez at gmail.com
Thu Apr 23 11:43:29 CEST 2015

```Nice. Thanks Chuck, I learnt something.

On 22 April 2015 at 23:45, Charles Z Henry <czhenry at gmail.com> wrote:

> On Wed, Apr 22, 2015 at 5:11 PM, Alexandre Torres Porres
> <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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