The effect of sampling and quantization on frequency estimation

The effect of sampling and quantization on frequency estimation for a single sinusoid is investigated. The Cramer-Rao bound for 1 bit quantization is derived, and compared with the limit of infinite quantization. It is found that 1 bit quantization gives a slightly worse performance, however, with a dramatic increase of variance at certain frequencies. This can be avoided by using 4 times oversampling. The effect of sampling when using non-ideal antialiasing lowpass filters is therefore investigated. Cramer-Rao lower bounds are derived, and the optimal filters and sampling frequencies are found. Finally, fast estimators for 1 bit sampling, in particular correlation based estimators, are derived. The paper concludes with simulation results for 4 times oversampled 1 bit quantization