## Brief Study of Dither A: Before Dither

Does it make sense to add noise to enhance the converter’s performance?

Dither – a puzzle to me for quite a long time. Recently I had time to read several related papers and APs. I would like to share some basic understanding (maybe still superficial…) here and as always to show some collected figures from the giants ;-).

Start by recommending an old seminal paper from 1984 [1] . Then write down a list of things which need to be known ‘before dither’:

• Sampling and quantization are the two inherent processes of ADC.
• With ideal sampling, no noise will be added to the signal. (Ideal sampling refers to sampling a band-limited signal at a frequency which is more than twice the bandwidth of the signal – Nyquist sampling rule.)
• Unlike sampling, quantization inherently adds noise to the signal. The part with dashed lines in Figure 1 indicates the error introduced by quantization:

Figure 1. Effect of sampling using finite quantization steps.

• For large amplitude or complex (complex here in terms of frequency content) signals, the quantization noise will be white [2].
• For low level or simple (simple here in terms of frequency content) signals, the quantization error cannot be treated as white noise added to the input signal. Here, in Figure 2, we take a large amplitude sinusoidal signal (this is a simple signal) as an example.

Figure 2: ADC inherently distorts signal [2]

• Distortion is greatest in small amplitude, simple signals. Here, in Figure 3, we take a 1-LSB Vpp sinusoidal signal centered on a threshold between two codes as an example. The reconstructed waveform looks like a square wave!

Figure3. Quantization in low-level signals resulting in severe error [2].

Reference

1. J. Vanderkooy and S. P. Lipshitz, Resolution below the least siginificant bit in digital systems with dither, J. Audio Eng. Soc., 1984.
2. Leon Melkonian, Improving A/D converter performance using dither, National Semiconductor (now TI), AN-804, 1992.
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