Digital Stochastic Measurement of a Nonstationary Signal With an Example of EEG Signal Measurement

This paper presents a method of digital stochastic measurement (DSM) of nonstationary signals. The method is based on stochastic analog-to-digital (A/D) conversion and accumulation, with a hardware structure based on a field-programmable gate array and a low-resolution A/D converter. The characteristic of previous implementations of DSM was the measurement of stationary signal harmonics. This paper shows how DSM can be extended and also used when it is necessary to measure the time series of nonstationary signals. An electroencephalography signal is selected as an example of a real nonstationary signal, and its DSM is tested by simulations and experiments. Tests are done without adding noise and with adding a noise-varying signal-to-noise ratio (SNR) from 10 to -10 dB. The results of simulations and experiments are compared versus theory calculations, and the comparison confirms the theory. The presented method provides control of the measurement uncertainty even at low SNR values, by controlling the sample rate of the used A/D converter. This enables designers of measurement systems to choose fast A/D converters with low resolution to achieve higher measurement accuracy.