Tag Archives: Statistical Signal Processing

Estimating parameters of periodic signals that are sampled with just two levels (0/1) in magnitude

P. Carbone, J. Schoukens and A. Moschitta, Quick Estimation of Periodic Signal Parameters From 1-Bit Measurements, IEEE Transactions on Instrumentation and Measurement, vol. 69, no. 2, pp. 339-353, Feb. 2020, DOI: 10.1109/TIM.2019.2902023.

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.

Methods for estimating periods of noisy signals

W. Fan, Y. Li, K. L. Tsui and Q. Zhou, A Noise Resistant Correlation Method for Period Detection of Noisy Signals, IEEE Transactions on Signal Processing, vol. 66, no. 10, pp. 2700-2710, DOI: 10.1109/TSP.2018.2813305.

This paper develops a novel method called the noise resistant correlation method for detecting the hidden period from the contaminated (noisy) signals with strong white Gaussian noise. A novel correlation function is proposed based on a newly constructed periodic signal and the contaminated signal to effectively detect the target hidden period. In contrast with the conventional autocorrelation analysis (AUTOC) method, this method demonstrates excellent performance, especially when facing strong noise. Fault diagnoses of rolling element bearings and gears are presented as application examples and the performance of the proposed method is compared with that of the AUTOC method.

Another paper about this in the same issue: 10.1109/TSP.2018.2818080.

Performing filtering on graphs instead of individual signals

E. Isufi, A. Loukas, A. Simonetto and G. Leus, “Autoregressive Moving Average Graph Filtering,” in IEEE Transactions on Signal Processing, vol. 65, no. 2, pp. 274-288, Jan.15, 15 2017. DOI: 10.1109/TSP.2016.2614793.

One of the cornerstones of the field of signal processing on graphs are graph filters, direct analogs of classical filters, but intended for signals defined on graphs. This paper brings forth new insights on the distributed graph filtering problem. We design a family of autoregressive moving average (ARMA) recursions, which are able to approximate any desired graph frequency response, and give exact solutions for specific graph signal denoising and interpolation problems. The philosophy to design the ARMA coefficients independently from the underlying graph renders the ARMA graph filters suitable in static and, particularly, time-varying settings. The latter occur when the graph signal and/or graph topology are changing over time. We show that in case of a time-varying graph signal, our approach extends naturally to a two-dimensional filter, operating concurrently in the graph and regular time domain. We also derive the graph filter behavior, as well as sufficient conditions for filter stability when the graph and signal are time varying. The analytical and numerical results presented in this paper illustrate that ARMA graph filters are practically appealing for static and time-varying settings, as predicted by theoretical derivations.