## 3 The Architecture of the Proposed ANN Model
#### Results of the Proposed ANN Model  
The real and predicted comparison values of cutoff frequency (\(f_{\text{c}}\)), stopband bandwidth (STBW), and insertion loss (IL) parameters for training and testing data are shown in Figure 10. As can be seen, the predicted data are obtained accurately. Ideally, the values predicted by the proposed model should be aligned closely with the real values. If the predicted values match the real values closely and follow the general trend of the data, the predicted dots will be located on the Y = X solid line, which suggests that the ANN model is a good fit for the data. On the other hand, if there are substantial differences between the predicted and real values, the predicted dots will be some distance from the Y = X solid line, which may indicate that the model is not capturing the relationship adequately or that there are other factors influencing the dependent variable that are not accounted for in the model. According to Figure 10, the predicted values are located approximately on the Y = X solid line for both training and testing processes, which indicates the precision and validity of the proposed ANN model. Figure 10: _Cont._  
Real and predicted testing and training values of \(f_{\mathrm{c}}\) (GHz), STBW (MHz), and IL (dB) parameters versus number of data samples in the proposed model are shown in Figure 11. As is seen, the circuit parameters are predicted accurately. Two samples are chosen for validation, and these are shown in Figure 11. The validation samples validate the accuracy of the proposed model and help to design the resonator with the desired parameters. Figure 10: Comparison between the real and predicted values for the training and testing data using the proposed model: (**a**)\(f_{\mathrm{c}}\) (GHz), (**b**) STBW (MHz) and (**c**) IL (dB). The real values are shown as solid lines. Real values are extracted values from EM-simulation of the filter, which are used to train and test the proposed model, while the predicted values are the parameters, which are predicted by the trained network. Figure 11: Real and predicted testing and training values of (**a**) \(f_{\mathrm{c}}\) (GHZ), (**b**) STBW (MHz), and (**c**) IL (dB) parameters versus number of data samples in the proposed model. The real values are shown as solid line. Real values are extracted values from EM-simulation of the filter. These are used to train and test the proposed model, while the predicted values are the parameters, which are predicted by the trained network. The real data of the training, testing, and validation procedures, obtained using the proposed model, are listed in Table 1. The final results of the proposed ANN model are listed in Table 2, which show high accuracy of the prediction for proposed model. The errors, which are reported in this table, correspond to the denormalized data. According to this table, the model is trained perfectly using the training data. The validation data are extracted from the proposed ANN model and are then used to design the equivalent filter for the proposed RRC with desirable parameters. As is seen in Table 1, the eight parameters of the filter dimensions are considered as the input parameters of the model and the three output parameters of the model are related to the results of the filter frequency response. Additionally, 23 samples and 6 samples are considered for the training and testing of the proposed model, respectively. Additionally, the validation sample verifies the results of the proposed model. Finally, the validation sample is simulated and fabricated, which demonstrates the validity of the predicted results expressed by the proposed ANN. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline  & \multicolumn{10}{c}{**Training Values and Design Parameters**} & \multicolumn{10}{c}{**Predicted Output**} \\  & \multicolumn{10}{c}{**Input Parameters**} & \multicolumn{10}{c}{**Real Output Param. **} & \multicolumn{10}{c}{**Param.