Quick Estimation of Periodic Signal Parameters From 1-Bit Measurements

Estimation of periodic signals, based on quantized data, is a topic of general interest in the area of instrumentation and measurement. Although several methods are available, new applications require low-power, low-complexity, and adequate estimation accuracy. In this paper, we consider the simplest possible quantization, that is, binary quantization, and describe a technique to estimate the parameters of a sampled periodic signal, using a fast algorithm. By neglecting the possibility that the sampling process is triggered by some signal-derived event, sampling is assumed to be asynchronous, that is, the ratio between the signal and the sampling periods is defined to be an irrational number. To preserve enough information at the quantizer output, additive Gaussian input noise is assumed as the information encoding mechanism. With respect to the published techniques addressing the same problem, the proposed approach does not rely on the numerical estimation of the maximum likelihood function but provides solutions that are very close to this estimate. At the same time, since the main estimator is based on matrix inversion, it proves to be less time-consuming than the numerical maximization of the likelihood function, especially when solving problems with a large number of parameters. The estimation procedure is described in detail and validated using both simulation and experimental results. The estimator performance limitations are also highlighted.