*5.4. Signal Processing*

The signals collected from the grinding tests were processed in MATLAB software. According to Ribeiro et al. [27], Moia et al. [63], and Lopes et al. [7], the AE sensor used in the tests has a frequency response of up to 300 kHz. However, as verified in the previous study of the same tests [29], the sensor presented significant frequencies up to 250 kHz. As shown by Freitas et al. [18], the PZT sensor has an efficient response of up to 200 kHz; the signal observed after this frequency has attenuations that can lead to erroneous results.

Considering the operational frequency bands of the sensors (up to 200 kHz for the PZT transducer and up to 300 kHz for the AE sensor), a digital bandpass filter (2 kHz to 300 kHz) was applied in order to eliminate noise. As there is a noise caused by the mechanical characteristics of the process and the data acquisition system, a digital Butterworth 10 order filter was also applied. The frequency of 2 kHz was chosen due to the fact that low frequencies present more information regarding noises than from the process. The signals were resampled at a rate of 1 MS/s, reducing the amount of data and respecting Nyquist's theorem. It is worth mentioning that the resample function of MATLAB applies an anti-aliasing low-pass FIR filter to the signals and compensates for the delay introduced by the filter. The STFT of each grinding test was computed with the following specifications: 5000-points rectangular window and 90% overlap. Thus, through Equations (2) and (3), the resolutions of 5 ms in time and 400 Hz in frequency were obtained.

Two frequency bands were chosen (one per sensor). The frequency bands were chosen based on the absolute values of the STFT spectrograms. Thus, the selected frequency bands presented two characteristics: (1) Frequency intervals with similar values over time (on the same spectrogram) and (2) magnitude differences (color bar) related to the process conditions (between spectrograms). Subsequently, the ROP metric was calculated for each frequency band. The absolute STFT values and the time–frequency resolution allowed the calculation of the ROP metric in the time domain. It is worth mentioning that the ROP metric is traditionally calculated in the frequency domain, so its calculation in the time domain, proposed in this paper, expands its application in real-time monitoring systems.

The magnitude-squared coherence (MSC) was then calculated for three grinding tests: 25 μm (slight), 105 μm (moderate), and 350 μm (severe). In addition, the upper envelope of each result was obtained in order to present the MSC results more clearly; the envelope was calculated by dividing the MSC results into 2048-point intervals, which correspond to about 1 ms time intervals from the total grinding pass section. Finally, the correlation between the measured surface roughness and the ROP mean values for both sensors was obtained by a linear regression. Signals were normalized in order to eliminate amplitude differences caused by the sensitivity of each sensor.
