  # 32 bit verses 24 bit, why? Some fun stuff here

Here is a fun table that illustrates why 24 bit is MORE than enough S/N for playback, and why 32 bit is used in digital editing. When we add, subtract, multiply and divide at 32 bit we don’t generate much truncation error. The chart, from Barry Thornton @ Austin Audio Works, is a nice and easy way to see the math table.

You TED SMITH experts on digital may comment, but I see bit depth @ 24-bit is plenty and up the sample rate instead of bit depth. We can’t exceed the physics on the S/N ratio at 20C past 24 bit.

Digital audio editing programs can often use sample sizes above their final product’s bit depth. Standard samples sizes of 20-bits, 24-bits, even 32-bit floating-point or long integer samples are now common, used to minimize fractional values and their attendant noise introduced when mixing or engaging in other mathematical processes on the samples.- Digital Audio Chapter Five: Quantization 2

The S/N ratio of a wire at room temperature is the floor limit of the atoms vibrations, and that is around minus 130 dBm (1 mW) or so for a 20C wire. We can’t get better than that theoretical value (see the math in the link). The chart is in dB ( a ratio) where the calculation is dBm, a decibel-based unit of power that is referenced to 1 mW. The watts at a –130 dB “ratio” are too small to even calculate accurately. - dBm to Watt Caluclator - everything RF

32-bit is more about rounding editing errors to be inconsequential than S/N ratio, 24-bit is plenty at a calculated minus 138 dB. Once 32-bit editing is done, we can be perfectly safe with 24-bit playback bit depth with a 144 dB dynamic range.

Thermal noise is generated as a result of thermal agitation of the charge carriers which are typically electrons within an electrical conductor. This vibration is dependent upon the temperature - the higher the temperature, the higher the agitation and hence the thermal noise level. There is a S/N calculator on the next page in the LINK below.

Thermal noise is one of the main limiting factors in a number of areas. In particular it limits the sensitivity of radio receivers because there is a noise floor below which it is not possible to proceed. Some receiver techniques are able to provide signal reception below the noise floor, but the data rate and other factors may be limited. It is therefore useful to be able to calculate the noise for any given instance.- RF Thermal Noise | Johnson-Nyquist Noise | Electronics Notes

Once bit depth is set for dynamic range and S/N the next thing is the ability to slice-up the data into smaller and smaller time based chunks to limit quantization errors. If two points are closer and closer together, a single data point can define the cord between the points better and better thus jitter is less and less.

Best,
Galen Gareis

5 Likes

Thanks for the splendid article.
I don’t understand the need of 24 bits in my living-room when it delivers me 138 dB.
That loud would probably kill me.
Jakob

We have two things, the lowest S/N ratio at a bit-depth, 16, 24 or 32, and the dynamic range at each bit depth. Once we hit the lowest S/N ratio that the atomic molecular vibrations allow at a temp and the dynamic range, it is better to concentrate on slicing up the sine wave more and more to better and better smooth it out.

The % distortion value is vanishingly low even at 16 bits, 0.0031%, so it is inconsequential and the 16-bit S/N is still -90 dB! 24-bit is as good as you’d ever need on playback. The data is why red book CD is decent sounding with a good analog master. It isn’t that bad.

I’d go with high sample rate 24-bit over 32-bit depth and lower sample rate every time for the reasons in the chart above. I’d go with 16-bit red book using decent analog sources over even that! The source always wins as you can’t make an analog source that is “worse” better in digital with more bit depth, just not worse.

Best,
Galen

I understand!
Thanks
Jakob