Effects of sampling and quantization on single-tone frequency estimation

The effects of sampling and quantization on frequency estimation for a single sinusoid are investigated. Cramér–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 four times oversampling. The effect of sampling when using nonideal antialiasing lowpass filters is therefore investigated through derivation of the Cramér–Rao lower bounds. Finally, fast estimators for 1-bit quantization, in particular, correlation-based estimators, are derived , and their performance is investigated. The paper is concluded with simulation results for fourtimes oversampled 1-bit quantization.