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This demonstration allows you to hear and see the improved audibility produced by dithering, as well as the increased noise floor. A dither is a small noise signal that is added to the quantization process. The dither signal is independently and randomly distributed, and has an amplitude approximately equal to the quantization step. Although the dither signal increases the noise floor, it also linearizes the quantization process, which theoretically allows for more precise quantization. A dither signal is an example of the current theory of stochastic resonance.
The following demonstration uses a 2 kHz sine wave quantized at 4 and 16 bits. The sounds are saved in Window's .WAV format, both 8 bit and 16 bit when necessary. The 4 bit resolution uses only 16 levels of the sound file. The dither signal is independently and normally (Gaussian) distributed with a standard deviation of a third of the quantization step. The spectrums display magnitude in dB versus frequency in kHz, and are calculated using the Fast Fourier Transform. All data was generated in MatLab. The demonstration is more effective if a good pair of speakers or headphones are used to listen to the sounds.
The results assume that the 16 bit resolution represents the "true" 2 kHz sine wave. The results show that, in the 4 bit resolution, the quantization process produces harmonic distortion. However, the addition of the dither removes this harmonic distortion, but also increases the noise level. Please let us know, which do you think sounds more like the 16 bit sine wave, the 4 bit sine wave with or without dither?
16 bit resolution
This resolution represents the true sine wave.
Listen to 16 bit 2 kHz sine wave (20k WAV)
4 bit resolution
Note the harmonic distortion producing a new pitch sensation.
Listen to 4 bit 2 kHz sine wave (10k WAV)
Listen to 16 bit then 4 bit 2 kHz sine wave (40k WAV)
4 bit resolution with dither
Note that the harmonic distortion has been removed, but the noise floor has been increased.
Listen to 4 bit dithered 2 kHz sine wave (10k WAV)
Listen to 16 bit then 4 bit dithered 2 kHz sine wave (40k WAV)
References
Lipshitz SP, Wannamaker RA, Vanderkooy J. (1992) "Quantization and dither: A theoretical survey." Journal of the Audio Engineering Society 40(5):355-75.
Vanderkooy J, Lipshitz SP. (1987) "Dither in digital audio." Journal of the Audio Engineering Society 35(12):966-75.
Vanderkooy J, Lipshitz SP. (1984) "Resolution below the least significant bit in digital systems with dither (Correction 32(11):889)." Journal of the Audio Engineering Society 32(3):106-12.
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