Advanced signal separation and recovery algorithms for digital x-ray spectroscopy

• Different algorithms are proposed for overcoming signal overlapping problem of x-ray spectroscopy.
• This spectrometer is used for in-situ applications for samples analysis.
• Statistical measurements are used for evaluation of the obtained results.
• DC-offset correction was done.
• Signal de-noising was implemented using four different methods.
• Three different approaches that allow correction of x-ray signal overlapping are presented.

X-ray spectroscopy is widely used for in-situ applications for samples analysis. Therefore, spectrum drawing and assessment of x-ray spectroscopy with high accuracy is the main scope of this paper. A Silicon Lithium Si(Li) detector that cooled with a nitrogen is used for signal extraction. The resolution of the ADC is 12 bits. Also, the sampling rate of ADC is 5 MHz. Hence, different algorithms are implemented. These algorithms were run on a personal computer with Intel core TM i5-3470 CPU and 3.20 GHz. These algorithms are signal preprocessing, signal separation and recovery algorithms, and spectrum drawing algorithm. Moreover, statistical measurements are used for evaluation of these algorithms. Signal preprocessing based on DC-offset correction and signal de-noising is performed. DC-offset correction was done by using minimum value of radiation signal. However, signal de-noising was implemented using fourth order finite impulse response (FIR) filter, linear phase least-square FIR filter, complex wavelet transforms (CWT) and Kalman filter methods. We noticed that Kalman filter achieves large peak signal to noise ratio (PSNR) and lower error than other methods. However, CWT takes much longer execution time. Moreover, three different algorithms that allow correction of x-ray signal overlapping are presented. These algorithms are 1D non-derivative peak search algorithm, second derivative peak search algorithm and extrema algorithm. Additionally, the effect of signal separation and recovery algorithms on spectrum drawing is measured. Comparison between these algorithms is introduced. The obtained results confirm that second derivative peak search algorithm as well as extrema algorithm have very small error in comparison with 1D non-derivative peak search algorithm. However, the second derivative peak search algorithm takes much longer execution time. Therefore, extrema algorithm introduces better results over other algorithms. It has the advantage of recovering and measuring over 21,941 peaks. Although, 1D non-derivative peak search algorithm has better extraction of peak height than other algorithms.