With the rapid development of the nuclear power industry on a global scale, the discharge of radioactive effluents from nuclear power plants and their impact on the environment have become important issues in radioactive waste management, radiation protection, and environmental impact assessments. \(\beta \) -detection of nuclides requires tedious processes, such as waiting for the radioactive balance of the sample and pretreatment separation, and there is an urgent need for a method specifically designed for mixing \(\beta \) rapid energy spectrum measurement method for nuclide samples. The analysis of hybrid \(\beta \) -energy spectrum is proposed in this study as a new algorithm, which takes advantage of the spectral analysis of \(\beta \) -logarithmic energy spectrum and fitting ability of Fourier series. The logarithmic energy spectrum is obtained by logarithmic conversion of the hybrid linear energy spectrum. The Fourier fitting interpolation method is used to fit the logarithmic energy spectrum numerically. Next, the interpolation points for the ‘effective high-energy window’ and ‘effective low-energy window’ corresponding to the highest \(E_\text {m}\) nuclide in the hybrid logarithmic fitted energy spectrum are set, and spline interpolation is performed three times to obtain the logarithmic fitted energy spectrum of the highest \(E_\text {m}\) nuclide. Finally, the logarithmic fitted spectrum of the highest \(E_\text {m}\) nuclide is subtracted from the hybrid logarithmic fitted spectrum to obtain a logarithmic fitted spectrum comprised of the remaining lower \(E_\text {m}\) nuclides. The aforementioned process is iterated in a loop to resolve the logarithmic spectra of each nuclide in the original hybrid logarithmic spectra. Then, the radioactivity of \(E_\text {m}\) nuclides to be measured is calculated. In the experimental tests, \({^{14}\hbox {C}}\) , \({^{90}\hbox {Sr}}\) , and \({^{90}\hbox {Y}}\) spectra, which are obtained using the Fourier fitting interpolation method are compared with the original simulated \({^{14}\hbox {C}}\) , \({^{90}\hbox {Sr}}\) , and \({^{90}\hbox {Y}}\) spectra of GEANT4. The measured liquid scintillator data of \({^{90}\hbox {Sr}}/{^{90}\hbox {Y}}\) sample source and simulated data from GEANT4 are then analyzed. Analysis of the experimental results indicates that the Fourier fitting interpolation method accurately solves \({^{14}\hbox {C}}\) , \({^{90}\hbox {Sr}}\) , and \({^{90}\hbox {Y}}\) energy spectra, which is in good agreement with the original GEANT4 simulation. The error in \({^{90}\hbox {Y}}\) activity, calculated using the actual detection efficiency, is less than 10% and less than 5% when using the simulated full-spectrum detection efficiency, satisfying the experimental expectations.
