Sampling rates and Efficiencies

The processing of the sampled data requires a limit on the data rates. The first device in this process is the analog to digital converter (ADC). Sampling speed (maximum bandwidth available) and the spacing of the quantization levels (quantization noise and conversion efficiency) are two parameters which are compromised to reach appropriate data rates. The bandwidth requirement is more straight forward and can be fairly easily specified given the science case use of the instrument. The number of bits and level spacing effects the noise level and thus efficiency where integration times are increased by the square of noise power increase. The ability to accurately produce a spectrum with interference present, or sloped band shapes is also a consideration. The Hagen and Farley, Radio Science 8, pp775-784 analyze the increase in integration time as a function of level spacing and oversampling parameters. This paper Thompson,Emerson and Schwab extend the analysis to odd and even multilevel sampling. A table of results list in the paper:

Efficiency Table

# of Levels Level Spacing [σ = 1,ε] \eta_Q = \sqrt{\frac{1}{\tau_r}}
2 (1 bit) - {\frac{2}{\pi}}
3 (2 bit) Odd 1.2224 0.809826
4 (2 bit) 0.995 0.881154
8 (3 bit) 0.586 0.962560
9 (3 bit) Odd 0.534 0.969304
16 (4 bit) 0.335 0.988457
32 (5 bit) 0.188 0.9986505
64 (6 bit) 0.104 0.998960
128 (7 bit) 0.0573 0.999696
256 (8 bit) 0.0312 0.999912

The number of levels is even if not specified, ε is in units of σ( the standard deviation of the input voltage), and \tau_r is the relative increase in integration time.

Spectrometer Resolution Requirements

\Delta \nu_c = (\frac{v_o}{c})\nu_o;

v_o = 1 km/s, \nu_o= 18 GHz, \Delta \nu_c = 60 KHz

\Delta \nu  = 2 GHz,

For \eta_Q = 0.9999 then 2 * 8*\Delta \nu bits/s per polarization per feed.

The correlator output data rate would then be \frac{ 32 Gb/s  } {N_{int}} per channel for \frac{ \Delta \nu  } { \Delta \nu_c } = 33K real data channels where {N_{int}} is the number of integrations.

Since ADC technology is such that FFT algorithms shall be implemented for spectrum generation. Currently 1.8 GHz ADC's are available with 8 bit sampling with 5 GHz technology on the horizon, ie

Canadian Proposal

Topic revision: r5 - 2009-10-19, CarolynWhite
This site is powered by FoswikiCopyright © by the contributing authors. All material on this collaboration platform is the property of the contributing authors.
Ideas, requests, problems regarding NRAO Public Wiki? Send feedback