Analysis of natural frequencies of bone-conducted sounds using short-time Fourier transform

This study presents a new method for evaluating the natural frequency of bone-conducted sounds using spectrograms obtained by short-time Fourier transform (STFT) and machine learning (ML) and examines its validity for practical applications. The natural frequency of bone-conducted sounds is conventionally evaluated using fast Fourier transform (FFT) analysis. Spectrograms obtained by STFT are used to visualize bone-conducted sounds as a two-dimensional time-frequency representation. Another advantage of spectrograms is that they facilitate the development of a convolutional neural network based ML model for predicting natural frequency. Forty-five healthy college students (20.36 ± 1.53 years) participated in this study, and five hammer impacts were applied to the right medial malleolus to record bone-conducted sounds generated at the right medial tibial condyle. Spectrograms were obtained from the recorded waveforms using STFT and input into a ML model trained with natural frequencies evaluated by FFT as a ground truth. The natural frequencies predicted by the ML model were compared with the natural frequencies evaluated by the FFT analysis. The mean absolute error was 12.92 ± 4.05 Hz, and the mean coefficient of determination (R2) was 0.845 ± 0.163, demonstrating the high evaluation accuracy of the proposed method. Feature analysis conducted using gradient-weighted class activation mapping revealed that the developed model focused on the peak sound pressure of the spectrogram when predicting the natural frequency. Further, it was found that the predicted values were large discrepancies from those evaluated by FFT analysis when the ML model failed to capture the peak sound pressure.