One-Bit Sine-Fit

This article introduces a novel procedure for the estimation of the frequency, amplitude, and phase of a sinusoidal signal after one-bit quantization. The estimator requires knowledge of the quantizer threshold but does not require information about the noise probability density function (PDF), possibly affecting measurement results. The threshold must be different from zero for estimating the amplitude but not necessarily for estimating the frequency or the phase. The algorithm requires an irrational value of the ratio between the sinusoidal frequency and the sampling rate. The procedure allows also the estimation of the noise variance and the cumulative distribution function (CDF). Theoretical properties are analyzed, and experimental results are provided to validate the estimation procedure.