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Fault tolerance and self-checking capabilities are key features of modern smart sensors, which often require the integration of additional signal processing facilities. In high-volume production areas such as automotive applications, however, optimized controllers are employed that typically have only limited computing resources. This paper examines several algorithms to assess the noise in a quasi-closed loop measurement channel under the assumption that the stimulus can be held constant during noise measurement. Starting from the definition of standard deviation, we propose several modifications and obtain an easy-to-implement algorithm relying entirely on addition and shift operations. Numerical experiments based on simulated and measured noise verify the practicability of the approach. The proposed algorithm has already been successfully implemented in a capacitive angular speed sensor system for automotive applications.