# How many bits? The real bit-depth of analog and digital recordings

(preliminary)

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*Sept 10, 2020*

What is the real bit-depth (resolution) of current and older recordings? How many bits does an analog recording need? And how many bits does the best digital recording take up? Do modern digital recordings exceed the limits of the CD? What is the problem with SNR measurements?

In digital systems the bit-depth (resolution) has an effect on the noise floor only and the accuracy of the digital representation is independent of the resolution (at least in digital systems with TPDF or Gaussian dither and the signal is higher than the noise floor). It means that any system which is limited by the noise floor (recordings, electronic components) has a well-defined bit-depth per sampling frequency and using this bit-depth in AD conversions or digital downconversions the noise floor doesn't change.

### SNR is not reliable

The standard signal-to-noise ratio (SNR) and dynamic range measurements don't reflect the real dynamic range of recordings. The ear is not an RMS meter and it detects noise in a different way and not as specified in the SNR measurements. The SNR and dynamic range measurement always overestimates the level of noise and the difference between the measured and the ear's dynamic range can be as high as 40 dB. Using perceptual weighting functions (e.g. the modified E-weighting curve used in 'Minimally Audible Noise Shaping' AES paper by Lipshitz, Vanderkooy and Wannamaker) can lower the gap between the measured SNR (or dynamic range) and the perceived dynamic range, but due the integrating nature of SNR measurements it also overestimates the noise. (This leads to the interesting discussion, that the dynamic range of even a standard 16 bit / 44.1 kHz audio is not 96 dB nor 93 dB, but higher than 100 dB!)

If we don't want to address perceptual questions (or at least not directly) then a simple 'comparative' method can be used. We can generate a 16bit/44.1 kHz wav file with standard TPDF dither and we can compare the noise floors of the recordings with this dither. Of course we have to be careful when comparing FFTs with different sampling rates, as the width of the FFT bins have to be equal and the FFT size has to be adjusted according to the sampling rate.

An overview of recording technologies and why 24 bit makes no sense:

Technology | Bit-depth standard | Bit-depth with noise shaping |

70's analog tape records (AAD & ADD) | 12.7 | 9.7 |
---|---|---|

80's analog tape records (AAD & ADD) | 13.8 | 10.8 |

80's digital tape records (DDD) | 14.3 | 11.3 |

16 bit/44,1 kHz TPDF dither | 16 | 13 |

Digital recording with the lowest noise | 18.2 | 15.2 |

16 bit/44,1 kHz with noise shaping | 19 | 16 |

**Standard bit-depth**: the noise floor is compared to the noise floor of a 16 bit/44,1 kHz TPDF dithered system. The bit-depth is calculated by converting the difference from decibels to bits. There is an alternative meaning of the 'standard bit-depth'. Let's take for example an analog recording with a noise floor equivalent to a noise floor of a 12 bit/44.1 kHz digital system or file. If this recording is transferred to 24 bit /44.1 kHz and truncated to 12 bits, then the noise floor of the original, the 24 bit version and the 12 bit version will be the same!

**Bit-depth with noise shaping**: Noise shaping extends the dynamic range with 18 decibels at sampling rate of 44.1 kHz - so the noise shaping lowers the bit requirement with 3 bits.

Modern digital recordings have much lower noise floor than recordings made with an analog tape, however the dynamic range of digital recordings still doesn't exceed the theoretical maximum of 16 bit/44.1 kHz.

* Csaba Horvath*