Research Pertaining To The Applicability Of Gaussian Function Windowed STFT To Internal-Combustion-Engine Vibroacoustic Signals

Among all the techniques used in joint time-frequency analysis of internal-combustion engine (ICE) vibroacoustic signals, the continuous wavelet transform (CWT) using complex Morlet wavelets, also called the analytic wavelet transform (AWT), is probably the most popular. The S transform (ST) has recently also become popular. In contrast, the earliest developed technique, the short-time Fourier transform (STFT), has been considered to be an ineffective tool probably because of its uniform resolution feature. The following work has been done centered around the applicability of Gaussian function windowed STFT to internal-combustion-engine vibroacoustic signals:The time-frequency localization ability of Gaussian function in digital time-frequency analysis was studied, and the condition to keep the optimal time-frequency resolution of the Gaussian window in the numerical implementation was obtained. Meanwhile, we put forward the idea to generate discrete-time Gaussian windows by the time standard deviation of its counterpart in the continuous-time domain, but not the sample number.The time-frequency resolutions of a Gaussian function windowed STFT were studied via numerical simulations. Based on the simulations, the limits for the time and frequency resolutions were determined. These can provide insights for window width selection, spectrogram interpretation and artifact identification.Analytical relationships between Gaussian function windowed STFT and AWT/ST have been derived. Gaussian function windowed STFT, AWT and ST were applied to both synthetic signals and some internal-combustion-engine vibroacoustic signals. The results indicate that:the time-frequency resolution limits also help interpreting AWT/ST spectra; moreover, the uniform resolution feature of STFT is not necessarily a disadvantage for time-frequency analysis of vibroacoustic signals when the engine is in stationary state and STFT with an appropriate window width can provide a time-frequency representation of better tradeoff between time and frequency resolutions.Based on the relationship between Gabor coefficient spectrum and the Gaussian function windowed STFT and the ability of the Gaussian-function windowed STFT linear spectrum to separate order components, an improved flowchart for Gabor order tracking (GOT) was formulated, which avoids blind search for appropriate analysis parameters, improving the degree of automation of the flowchart, and guarantees the precision of waveforms reconstructed by GOT.