Dither#Digital audio

Dithering (English for " trembling" ) describes a method that can mitigate the effect of quantization errors in digital audio technology. These errors occur both in the digitization as well as in digital arithmetic operations with signals. Instead of disturbing distortions produced a less disruptive uniform noise, similar to that of an analog amplifier.

The problem: systematic rounding errors

Without dithering, the putative quantization error signal is his name only fair that if the useful signal from sample to sample, typically by several quantization levels altered, both at high levels, with not too low frequencies. Then the following error each other are mutually statistically independent, so that the quantization noise manifests itself as a broad-band white noise. As a relatively small base to the useful signal, it is hardly noticed, see typical system dynamic range.

With decreasing modulation not only the masking of noise by the useful signal will be slight, see signal -to-noise ratio, but for typical, orderly useful signals such as music occur correlations of the quantization error, in particular to each other have the following quantization sections same sign, so that the noise energy shifted to lower frequencies and audible concentrated in spectral lines. These lines are harmonics and intermodulation frequencies in the useful signal. Blame for this distortion is the nonlinearity of the quantization.

A solution: random round up or down

By adding a suitable dither noise to the signal itself does increase the noise energy, but the characteristic is linearized so that the distortion disappears and very quiet signal components better (or at all only ) are perceived. The dither noise consists of random values ​​from a range of the order of a quantization level. There are various probability distributions (PDF, probability density function) applied for noise values ​​. The minimum noise ( with respect to the variance of the PDF ), which must be added for a complete Linearsierung the characteristic is uniformly distributed ( rectangular, RPDF dither ) exactly one step height. This is in the quantization randomly rounded up or down, at what height the signal value between two stages is associated with a probability that depends linearly from it.

RPDF dither acts as a pulse width modulation, to the random aspect. These may be waived in connection with oversampling, if the resultant artifacts are inaudible at high frequencies, compare sigma -delta converter and noise shaping.

More dither types have triangular densities ( TPDF dither, triangular ) and Gaussian densities ( GPdf dither ). In music signal processing is TPDF dither has prevailed, as he explains how the RPDF dither the characteristic of completely linearized and in addition has a constant noise power, regardless of the input signal value. The noise power is 4.77 dB with only slightly higher than the RPDF dither.

Application

Dither found in various areas of digital audio technology application in which the signal is " resampled " is: When mastering, when using older sampler with reduced dynamics ( for example, 8 bits), or in the editing with effects units, a higher dynamic range than the have CD - standard 16-bit.

Rather than simply cut off the " excess " bits ( " truncation " ), for example if a 24-bit - 16-bit signal to a - signal is converted, the dither should be added, since otherwise the problem of the quantization error as described above occurs again. Most reverbs work internally with much higher -resolution floating-point or with dithering.

The example of a Bittiefenreduktion of a 24-bit word length on the usual 16-bit word length of an audio CD is measurable, that dithering especially in low resolution levels receives much more information, thus increasing the dynamic range of the desired signal. Figure 1 shows the signal after Bittiefenreduktion without dithering. You can clearly see the quantization in the form of overtones. Figure 2 shows the Bittiefenreduktion turning dithering. Although you can now see the existing noise floor, but this is at a large distance to the useful signal and psychoacoustic no longer perceived as a distortion of the desired signal.