Quantization Efficiency

Quantization is a nonlinear process which generates additional frequency components (Thompson et al. 1986). This means that the signal is no longer band-limited, so the Sampling Theorem no longer holds. If a signal is sampled at the Nyquist Frequency, information will be lost. Therefore, sampling faster than the Nyquist Frequency results in detection of more of the signal and a lower signal-to-noise ratio [SNR]. Let $\beta$ be the Oversampling ratio and define

$$\eta_Q \equiv {{\rm SNR}_{\rm quant}\over{\rm SNR}_{\rm unquant}}.$$

Then the following table gives values of $\eta_Q$ for a number of parameters.

Quantization Levels	$\eta_Q (\beta=1)$	$\eta_Q (\beta=2)$
2	0.64	0.74
3	0.81	0.89
4	0.88	0.94

The Very Large Array of 27 radio telescopes in Socorro, New Mexico uses three-level quantization at $\beta=1$, so $\eta_Q = 0.81$.

References

Thompson, A. R.; Moran, J. M.; and Swenson, G. W. Jr. Fig. 8.3 in Interferometry and Synthesis in Radio Astronomy. New York: Wiley, p. 220, 1986.