Simple method for background subtraction in gamma-ray spectra

The peak-free spectrum I_b(n) can be obtained by transform $\text{I}{}_{\mathrm{<mtext>b</mtext>}}\text{(n) =}\text{S}\text{̂}{}_{\mathrm{<mtext>k</mtext>}}\text{(I(n)-q¦}\text{d}{}^{\mathrm{m}}\text{I(n)/}\text{d}\text{n}{}^{\mathrm{m}}\text{¦)}$ of initial spectrum I(n), where $\text{S}\text{̂}{}_{\mathrm{<mtext>k</mtext>}}$ is the operator of linear smoothing and q ≈ 0.5 σ if m = 1 and q ≈ 0.2 σ² if m = 2, σ is the full width at half maximum for peaks.