Measurement of Power Density at Zero Frequency With a Trend Compensation

The noise power spectrum (NPS) at zero frequency can represent a global noise property of a system and is the sum of the covariances with lags. As the lag increases, an estimate of the sum shows a converging curve. However, due to the unpredictable signal trend, the estimate continues to increase. In this paper, a trend model is first introduced to describe the trends. A high-precision estimate algorithm for zero-frequency NPS is then proposed based on a Blackman-Tukey method with a rectangular window, in which windowed periodograms are sample averaged as the Bartlett-Welch method. In order to analyze the covariance and trend components, sequential observations on estimates are conducted with respect to the periodogram and window sizes. Through the analysis, an appropriate range of the window sizes is suggested and a trend-compensation scheme is developed. Experimental results for x-ray images acquired from a radiography detector showed that an estimate precision was improved to 2.63% from 49.1% of a conventional approach with 99.5% covariance components.