## 2 Theory and Analysis  
### Radiation Emission Components  
As mentioned above, radiated electromagnetic emission is an inherent characteristic of the equipment. Therefore, the electromagnetic radiation test data of a piece of electronic equipment is a kind of inherent property corresponding to the equipment. Hence, by extracting the inherent characteristics from the electromagnetic emission spectrum test data, the electromagnetic emission of a piece of electronic equipment can be identified. Whole emission spectrograms contain too much information to be compared. Directly obtained radiated emission test data have the characteristics of a wide frequency band, a large amount of data, and information redundancy, containing some data that cannot reveal the physical characteristics and essential attributes of EUT. Hence, modeling the entire set of radiation emission data will lead to the complexity of the mathematical tools and the need for a large number of testing data. It is necessary to filter features that can characterize the physical characteristics of the test object, while further reducing the feature dimensions. In the circuit inside the electronic equipment, many periodic signals (such as clock signals or oscillator output signals) generated by basic excitation source signals will inevitably generate high-frequency periodic signals or nonlinear components after direct coupling, mixing, or modulation [36; 41; 42]. In [31], by sorting the most common circuits and their electromagnetic emission, the authors presented a creative theory (BEWT) stating that the basic waveforms can be summarized using four categories in the time domain: the square wave, sine wave, damped oscillation, and the spike wave. These four waveforms and their corresponding spectra are shown in Figure 1. The authors argued that most complex electromagnetic emissions are the result of both basic emission waveforms and their interaction with the periphery circuits, such as mixing or modulation, on a physical level. The newly generated spectral components can still be regarded as four basic emission waveforms. Hence, the electromagnetic emissions of complex systems can be constructed by means of the four basic waveforms. Figure 1: Schematic diagram of four basic waveforms: (**a**) sine wave, (**b**) square wave, (**c**) damped oscillation, and (**d**) spike wave. It is assumed that \(V(f)\) is the emissions spectrum of a complex system, \(V(f)\), which is expressed as follows in [36]:  
\[V(f)=\sum_{i=1}^{p}H_{i}(f_{h})\oplus\sum_{j=1}^{q}N_{j}(f_{t})\oplus E(f)\oplus S (f)\oplus v_{t}(f)\oplus\zeta \tag{1}\]  
where \(v_{t}(f)\) is the original noise floor of the measurement system; \(H_{i}(f_{h})\) represents the harmonic points, which are generated by square waveforms; \(N_{j}(f_{k})\) represents the narrowband points, which are generated by sine waveforms; and \(E(f)\) and \(S(f)\) represent the lift of the spectrum caused by damped oscillation and spike waves, respectively. Moreover, \(\zeta\) is the residue. \(\oplus\) in Equation (1) denotes a superposition in the view of physical states, including not only the amplitude superposition of the same frequency signals but also the effects between different signals, such as intermodulation, mixing response, etc., shown as in Figure 2.  
Observing Figure 1a,b, \(H_{i}(f_{h})\) and \(N_{j}(f_{k})\) can be viewed as a series of peak signals in the frequency spectrum. Furthermore, from the view of the frequency spectrum, isolated \(E(f)\) and \(S(f)\) features can be regarded as a single waveform with a bandwidth, as shown in Figure 1c,d. In our paper, the advantage of distinguishing \(H_{i}(f_{h})\) from \(N_{j}(f_{k})\) is not significant, and the advantage of distinguishing \(E(f)\) from \(S(f)\) is also not significant. Thus, to reduce the number of input variables in the classification and identification method proposed in this paper, only three groups of radiation emission components were extracted from the whole spectrum.