Influence of Signal Stationarity on Digital Stochastic Measurement Implementation

Abstract

The paper presents the influence of signal stationarity on digital stochastic measurement method implementation. The implementation method is based on stochastic voltage generators, analog adders, low resolution A/D converter, and multipliers and accumulators implemented by Field-Programmable Gate Array (FPGA). The characteristic of first implementations of digital stochastic measurement was the measurement of stationary signal harmonics over the constant measurement period. Later, digital stochastic measurement was extended and used also when it was necessary to measure timeseries of non-stationary signal over the variable measurement time. The result of measurement is the set of harmonics, which is, in the case of non-stationary signals, the input for calculating digital values of signal in time domain. A theoretical approach to determine measurement uncertainty is presented and the accuracy trends with varying signal-to-noise ratio (SNR) are analyzed. Noisy brain potentials (spontaneous and nonspontaneous) are selected as an example of real non-stationary signal and its digital stochastic measurement is tested by simulations and experiments. Tests were performed without noise and with adding noise with SNR values of 10dB, 0dB and - 10dB. The results of simulations and experiments are compared versus theory calculations, and comparasion confirms the theory

An FPGA-Based Solution for Computing a Local Stationarity Measure From Satellite Data

“…To the best of our knowledge, reports of such FPGA implementations are rare in the scientific literature. The work described in [11], which presents an FPGA implementation of a digital stochastic measurement method, is related to the stationarity problem, but it is applied to the theory of measurement in general and to brain signals in particular.…”

Influence of Wilbraham-Gibbs Phenomenon on Digital Stochastic Measurement of EEG Signal Over an Interval

“…When the Fourier sums are calculated for a function, the Wilbraham-Gibbs phenomenon [26][27] includes both the fact that Fourier sums overshoot at the function jump discontinuity, and that this overshoot does not decrease as the fundamental frequency increases [28]. According to the Wilbraham-Gibbs phenomenon, at any jump point of a piecewise continuously differentiable function with a jump of a, the n th partial Fourier series will (for very large n) overshoot this jump by approximately a⋅(0.089490...) at one end and undershoot it by the same amount at the other end [28].…”

“…Measurement uncertainty in [25] is calculated by the developed theory while the EEG signal is selected as an example of real nonstationary signal. Digital stochastic measurement of EEG signal harmonics is tested by simulations and by experiments in [25,26]. Tests are done both without adding noise and with adding noise (SNR varies from 10dB to -10 dB).…”

“…Papers [25,26] are the result of researching alternative solutions for such situations of a high-level ambient noise presence, and they describe the implementation of the DSM approach in measurement of non-stationary signal harmonics with varying measurement time. Measurement uncertainty in [25] is calculated by the developed theory while the EEG signal is selected as an example of real nonstationary signal.…”