Uncertainty evaluation model for sampling based instruments

A model was developed to evaluate the combined uncertainty of sampling based instruments. This paper analyzes the measurement uncertainty sources caused by the quantization error, offset error, gain error and integral nonlinearity error in data acquisition, as well as the measurement uncertainty sources in the fixed-point and floating-point operations by the digital signal processor with finite word-length. The propagation model of all the uncertainty sources in the data acquisition and signal processing through the discrete Fourier transform algorithm was studied based on the above results. Simulations illustrate the validity of the presented analytical expression between the combined standard uncertainty and the analogue to digital conversion bits, the fix-point or float-point operation bits, the signal-noise ratio and the sample number.