## 2 Materials and Methods
### Participants  
An a priori sample size estimation was performed in G*Power [48], assuming a statistical power of 0.80 and a significance level of 0.05. For a one-way ANOVA with three groups and a moderate effect size ([PERSON]'s d = 0.05), the study required a minimum sample size of 42 participants. However, to ensure robustness and address potential limitations, sixty participants diagnosed with type 2 DM were recruited from the Professor Polytoro Ernany University Hospital of the Federal University of Santa Catarina--HU/UFSC/EBSERH (see Table 1). The inclusion criteria specified that participants were 18-75 years old and of any gender. The exclusion criteria included the diagnosis of retinopathy, chronic infectious or inflammatory diseases, use of an implantable electronic device (e.g., a cardiac pacemaker), and use of drugs that can affect cardiovascular function (e.g., beta-blockers). The institutional research ethics committee approved the study (protocol number 3.326.385), and participants only entered the study after informed consent. The anthropometric and clinical data (e.g., age, DM duration, use of medications, presence of complications, and the last results of the glycated hemoglobin (HbA1c) test--a \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **noCAN** & **subCAN** & **estCAN** \\ \hline n & 20 & 20 & 20 \\ Age (yrs) & 60.1 \(\pm\) 4.5 & 62.0 \(\pm\) 7.0 & 57.0 \(\pm\) 8.4 \\ Gender & 7F/13M & 12F/8M & 10F/10M \\ DM duration (yrs) & 13.2 \(\pm\) 9.5 & 13.9 \(\pm\) 9.8 & 17.6 \(\pm\) 9.3 \\ HbA1c (mmol/mol) & 89 \(\pm\) 22 & 71 \(\pm\) 31 & 99 \(\pm\) 19 \\ \hline \hline \end{tabular} Note: Values are presented as mean \(\pm\) SD. Abbreviations; DM—diabetes mellitus; noCAN—individuals with type 2 DM without cardiac autonomic neuropathy; subCAN—individuals with type 2 DM with subclinical cardiac autonomic neuropathy; subCAN—individuals with type 2 DM and established cardiac autonomic neuropathy; HbA1c—glyocated hemoglobin.  
\end{table} 
Table 1: Demographic and clinical data of the participants. Figure 1: A block diagram illustrating the proposed methodology for investigating cardiovascular autonomic neuropathy (CAN) in individuals with type 2 diabetes mellitus (T2 DM) through the application of empirical mode decomposition (EMD) to heart rate variability (HRV) signals. The participants’ electrocardiogram (ECG) and photoplethysmography (PPG) signals were collected. In the pre-processing stage, the ECG signals underwent bandpass filtering, followed by the derivation of the HRV signals. The feature extraction stage involved applying EMD to the HRV signals to obtain the first four intrinsic mode functions (IMFs) components. From these IMFs, the following features were calculated: \(ASR_{area}\)—area of the analytical signal; \(SODP_{area}\)—area of the second-order difference plot; \(SODP_{CTM}\)—the central tendency measure of the second-order difference plot; \(PSD_{plump}\)—peak amplitude of the power spectral density estimation; \(PSD_{prou}\)—band power of the power spectral density estimation; and \(PSD_{nfreq}\)—mean frequency of the power spectral density estimation. The final stage involved conducting the statistical analysis to compare the mean differences of all the features among the different CAN severity level groups: noCAN—individuals with T2 DM without CAN; subCAN—individuals with T2 DM and subclinical CAN; and estCAN—individuals with T2 DM and established CAN. The PPG signal was used for CAN classification purposes. blood test that shows the average blood sugar (glucose) level over the past two to three months) were obtained from previous ECG and photoplethysmography (PPG) data. The participants were given cardiac autonomic reflex tests (CARTs) and baroreflex sensitivity (BRS) analyses to classify them into three levels of CAN (i.e., noCAN--no presence of CAN, subCAN--subclinical CAN, and estCAN--established CAN). The CARTs comprised tests for heart rate response, including the RR interval to pac breathing, the Valsalsalva maneuver, and postural change from lying to standing [4].