The introduction to quantization and quantization error showed that the quantization error is correlated with the input signal. Athough this can be desirable for a distortion-like audio effect, it can be a problem in analog-digital conversion and bit-depth conversion.

Dither can be used to decorrelate the signal and the noise - it is additional noise that is added to the input signal before the quantization.

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Quantization Error¶

The quantization error $e = x-x*$ shows a more stochastic bahavior in the time domain the the error without dither:

PDF of the Error¶

The PDF of the error after dithering is more uniformly distributed:

Spectrum¶

The noise-floor is clearly visible in the spectrum. However, the higher partials of the distortion through quantization disappear:

Noise Shaping¶

While the applied dither does change the qualities of the quantization, it does not necessarily improve them a lot for the 3-Bit case. The noise - though now uncorrelated, is very dominant with this low SNR. Noise shaping uses filters to shape the dither. If the sampling rate is high enough, it can be moved to frequncies outside the human hearing.

The plot below shows a high-pass filter with a cutoff frequency of $f_c = 0.7 f_s = 16800 \mathrm{Hz}$ and a steep slope (7th order Butterworth):

The spectrum of the resulting signal shows a noise-floor that is rising towards higher frequencies.