Dithering (audio technology)
Dithering ( Engl. For "trembling") describes a method that the effect of the digital audio technology quantization can mitigate. These errors occur both in digitization and in digital arithmetic operations with signals. Instead of annoying distortion, the result is a less annoying, uniform noise that is similar to that of an analog amplifier .
The problem: systematic rounding errors
Without dithering, the error signal known as quantization noise only lives up to its name if the useful signal typically changes by several quantization levels from sample to sample, i.e. with high modulation with frequencies that are not too low. Successive errors are then statistically independent of one another, so that the quantization noise is presented as broadband white noise . As a small background relative to the useful signal, it is hardly perceived, see typical system dynamic values .
With decreasing modulation, not only is the masking of the noise by the useful signal lower, see signal-to-noise ratio , but for typical, ordered useful signals such as music, correlations of the quantization error occur; In particular, successive quantization errors have the same sign in sections , so that the noise energy shifts to lower frequencies and is clearly audibly concentrated in spectral lines. These lines are harmonics and intermodulations of the frequencies in the useful signal. This distortion is ultimately due to the non-linearity of the quantization characteristic .
One solution: round up or down at random
Adding suitable dither noise to the signal increases the noise energy, but the characteristic curve is linearized so that the distortions disappear and very quiet signal components are better (or at all) perceived. The dither noise consists of random values from a range on the order of a quantization level. Different probability distributions (PDF, probability density function ) are used for the noise values. The minimum noise (with regard to the variance of the PDF) that has to be added for a complete linearization of the characteristic curve is evenly distributed (rectangular, RPDF dither) over exactly one step height. This means that the quantization is randomly rounded up or down, with a probability that is linearly dependent on the height of the signal value between two levels.
RPDF dither works like a pulse width modulation , except for the random aspect. This can be dispensed with in connection with oversampling if the resulting artifacts are inaudibly high frequencies, compare sigma-delta converter and noise shaping .
Further dither types have triangular densities (TPDF dither, triangular ) and Gaussian densities (GPDF dither). In music signal processing, TPDF dither has established itself because, like the RPDF dither, it completely linearizes the characteristic curve and also has a constant noise power, regardless of the input value of the signal. At 4.77 dB, the noise power is only slightly higher than with the RPDF dither.
application
Dithering is used in various areas of digital audio technology, always when the signal is processed and then the bit depth is reduced and / or the sampling rate is changed: when mastering , when creating audio files (WAV or MP3) from DVDs, when using them older sampler with limited dynamics (e.g. 8 bit), or after processing with effects devices . The result is often a CD-quality signal with the usual 16 bit and 44.1 kHz.
Instead of simply cutting off the "superfluous" bits (" truncation ") or rounding them ( round to even ), if z. If, for example, a 24-bit signal is converted into a 16-bit signal, dithering should be used, as otherwise the quantization error described above occurs. Considered clearly, the noise in connection with a rounding leads to a signal that corresponds to the previous value in the long term. The missing bits can be partially reconstructed by filtering and averaging. Effects devices and audio software often work internally with significantly higher resolution 32-bit integer or 32-bit floating point numbers . Dithering should then be used for the reconversion.
Using the example of a bit depth reduction from a 24-bit word length to the usual 16-bit word length of an audio CD, it can be measured that dithering enables significantly more information, especially at low levels, and thus increases the dynamic range of the useful signal. Figure 1 shows the signal after bit depth reduction without dithering. You can clearly see the quantization distortion in the form of overtones . Figure 2 shows the bit depth reduction with activated dithering. You can now see the existing noise floor, but at a large distance from the useful signal, it is no longer correlated with it and is no longer perceived psychoacoustically as a noticeable distortion of the useful signal.
When using high sampling rates, the noise can be shifted to higher areas of the spectrum so that it is completely filtered during a later conversion. This process can be clearly described by the fact that there is a finer level of shaking. Low-frequency components in the signals can thus be almost completely reconstructed.
literature
- Michael Dickreiter, Volker Dittel, Wolfgang Hoeg, Martin Wöhr (eds.), "Handbuch der Tonstudiotechnik", 8th, revised and expanded edition, 2 volumes, publisher: Walter de Gruyter, Berlin / Boston, 2014, ISBN 978-3- 11-028978-7 or e- ISBN 978-3-11-031650-6
- Ken C. Pohlmann: Principles of Digital Audio. 4th edition. McGraw-Hill, New York NY et al. 2000, ISBN 0-07-134819-0 .
- Thomas Sandmann: Effects & Dynamics. The salt in the soup of every music mix. Technique and practice of effects and dynamics processing. (Now with surround effects). 3rd, expanded edition. Presse Project Verlag, Bergkirchen 2003, ISBN 3-932275-57-8 .
- Robert A. Wannamaker, Stanley P. Lipshitz, John Vanderkooy, J. Nelson Wright: A Theory of Non-Subtractive Dither. University of Waterloo, Waterloo 2000 ( PDF; 347 kB ).
- Michael Warstat, Thomas Görne: studio technology. Background and practical knowledge. 5th edition. Elektor-Verlag, Aachen 2001, ISBN 3-928051-85-7 .
- John Watkinson: The Art of Digital Audio. 3rd edition. Focal Press, Oxford et al. 2001, ISBN 0-240-51587-0 .
- Udo Zölzer: Digital audio signal processing. 3rd, revised and expanded edition. Teubner, Stuttgart et al. 2005, ISBN 3-519-26180-4 .
- Manfred Zollner, Eberhard Zwicker : Electroacoustics. 3rd, improved and enlarged edition. Springer, Berlin et al. 1998, ISBN 3-540-64665-5 .
- Dieter Stotz: Computer-aided audio and video technology. 2nd Edition. Springer, Berlin et al. 2011, ISBN 978-3-642-23252-7 .