## 4 Simulation and Experiment
### The Simulation to Verify Applicability and Experimental Test  
The simulation waveform is shown in Figure 4, which consists of a strong peak, a sub-strong peak adjacent to the strong peak, and a weak peak far away from them. The total number of addresses is 120. The peak data were generated by Gaussian linear function, the peak addresses were 51, 57, 87; and the FWHM were 6, 4, 6, respectively. Gaussian white noise with SNR = 10 dB is added to the data through \"awgn\" function in MATLAB. Three methods were used to search peaks, respectively, which verified that ISZAC was  
Figure 3: Accuracy verification diagram.  
superior to SZAC in applicability, and different types of peaks could be identified without modifying parameters.  
Figure 4a shows the results of SZAC with \(m=2\), \(H_{\text{G}}=6\), and \(T_{0}=1.5\). The overlapping peak was identified by the narrow window function, but the third peak could not be identified effectively due to the influence of noise. The threshold processing result of the address was \(T(87)=0.75\).  
Figure 4b shows the results of SZAC with \(m=5\), \(H_{\text{G}}=6\), and \(T_{0}=1.5\). The wide window function is used to identify the third peak affected by noise, but the overlapping peak near the strong peak cannot be effectively identified, and the threshold processing result of this address is \(T(57)=0.99\). In Figure 4a,b, the comparison function with \(cmpN=1\) is introduced to eliminate the misidentification results.  
Figure 4c shows the results of ISZAC, and parameter settings are consistent with the aforementioned experiments. The ISZAC method was used to identify the three peaks effectively.  
Figure 4: Applicability verification diagram.  
The Narrow window zero-area conversion function has a strong ability to identify overlapping peaks, while the wide window function is beneficial in suppressing noise interference. ISZAC selects multiple conversion functions to give full play to the advantages of each type of conversion function. There is no need to set different parameters according to the input spectrum, which improves the limitation of SZAC parameter setting depending on the spectral data characteristics and experience.  
The measured effect of the XRD pattern is shown in Figure 5. The crystal composition of the coal sample includes kaolinite and lithium, with Li accounting for 68.9%. The X-ray diffractometer model is D8, copper target material, voltage 35 KV, current 30 mA, and step size 0.02. Figure 5a shows the results of ISZAC, and the parameter settings are consistent with the above experiments. The peak searching results are basically consistent with the PDF of the two crystal components, and the ISZAC measurement effect is efficient.  
Figure 5b shows the results of SZAC with \(m=2\), \(H_{G}=6\), and \(T_{0}=2\). The number of peaks determined in the recognition result is more than that in the ISZAC, because it misjudges some addresses caused by noise as a peak. Observe the local magnification map of \(2\theta=[5.5,8]\). The spectral waveform in this range fluctuates greatly, and the peak width at the misidentified address is insufficient. Compared with PDF, it can also be found that there is no peak in this range, and the narrow window function is easily affected by noise, resulting in over-recognition.  
Figure 5c shows the results of SZAC with \(m=5\), \(H_{G}=6\), and \(T_{0}=2\). The over-recognition situation is significantly reduced under the wide window function. Observe the local magnification map of \(2\theta=[37.5,40]\) and PDF. There are unrecognized Kaolinite diffraction peaks in this range. The wide window function suppresses the noise interference but causes the phenomenon of missing recognition. It must be pointed out that the comparison function with \(cmpN=1\) is introduced in Figure 5b,c to eliminate the misidentification results.