Peaks (version 0.2)

SpectrumSmoothMarkov: Suppression of statistical fluctuations with discrete Markov chain.

Description

This function calculates smoothed spectrum from source spectrum based on Markov chain method.

Usage

SpectrumSmoothMarkov(y,window=3)

Arguments

y

numeric vector of source spectrum

window

width of averaging smoothing window

Value

• Numeric vector with smoothed spectrum.

encoding

latin1

Details

The algorithm is based on discrete Markov chain, which has very simple invariant distribution: $$U_2=\frac{p_{1,2}}{p_{2,1}}U_1$$ $$U_3=\frac{p_{2,3}}{p_{3,2}}U_2 U_1$$ $$\ldots$$ $$U_n=\frac{p_{n-1,n}}{p_{n,n-1}}U_{n-1} \ldots U_2 U_1$$ and $U_1$ being defined from the normalization condition: $$\sum_{i=1}^{n}U_i=1$$ $n$ is the length of the smoothed spectrum.

The probability of the change of the peak position from channel $i$ to the channel $i+1$ is : $$p_{i,i \pm 1}=A_i \sum_{k=1}^{m}exp \left( \frac{y(i \pm k)-y(i)}{y(i \pm k)+y(i)}\right)$$ where $A_i$ is the normalization constant so that: $$p_{i,i-1}+p_{i,i+1}=1$$

and $m$ is a width of smoothing window.

References

Z.K. Silagadze, A new algorithm for automatic photopeak searches. NIM A 376 (1996), 451.