*5.3. Signal Processing and Selection of Frequency Bands*

The data sets from the grinding tests were digitally processed in MATLAB software. Two distinct signals were acquired in the tests, the first signal refers to the set of chirp waves of the emitter PZT, while the second signal refers to the chirp waves collected by the receiver PZT. The emission was composed of five chirp signals sent by the emitter PZT and the reception was composed by fives signals acquired by the receiver PZT. The signals collected by the receiver, for each grinding pass and depth of cut, were divided into data vectors or packages, resulting in five packages.

The spectral analysis of the packages corresponding to the receiver signals was performed in order to find the frequency band that best characterize the workpiece conditions (without material removal and with material removal). The Fast Fourier Transform (FFT) was used to analyze the spectral content of the receiver PZT signals. The FFT magnitude was computed for each received vector and then the mean values were obtained. The criterion used for the selection of frequency bands was presented by Ribeiro et al. [16], in which the best frequency bands are those with the greatest differences in magnitudes and minimum overlap between the observed conditions.

After the selection of frequency bands, Butterworth digital filters were applied to the received packages and new vectors were obtained. Then, the RMS and Counts values were calculated for both vectors (raw unfiltered and filtered received signals). Intervals of 4096-point, corresponding to 1 ms, as reported by Webster et al. [51], were used to compute the RMS and Counts values.

Finally, the standard deviation and mean values for each received package and workpiece condition (without material removal, first grinding pass, second grinding pass and third grinding pass) were computed. It is worth mentioning that the threshold used in the Counts statistic was selected based on the noise level of the receiver signals. The flowchart presented in Figure 4 shows the digital signal processing scheme. In order to correlate the mean values of the statistics (RMS and Counts) with the volume of material removed, a linear regression was calculated. Thus, through the coefficient of determination (*R*) it was possible to infer the degree of correlation between the values obtained with the proposed technique and the volume of material removed. The values were normalized before the computation of the linear regression in order to eliminate the amplitude differences between the two statistics. The application of linear regression as a correlation metric can be found in several scientific works, as in de Oliveira Conceição Jr. et al. [67] and Viera et al. [21].

**Figure 4.** Flowchart of the digital signal processing scheme.
