A data-science team is analyzing 48 kHz vibration data from a gearbox to catch early bearing defects. The defects manifest as very short, non-stationary bursts between 3 kHz and 6 kHz that must be located in time while still preserving their spectral content for feature extraction. Which signal-processing technique is the most appropriate first step to satisfy these requirements?
Perform a discrete Fourier transform on the entire 60-s record and inspect the magnitude spectrum
Apply a short-time Fourier transform with a fixed 50 ms Hamming window
Fit a 40-order autoregressive model to the signal and analyze the residuals
Compute the continuous wavelet transform using a Morlet mother wavelet
A continuous wavelet transform (CWT) provides joint time- and frequency-localization and performs a multi-resolution analysis, so transient events can be isolated without sacrificing spectral detail. A fixed-window short-time Fourier transform delivers only one time-frequency trade-off, the whole-record DFT loses all temporal information, and high-order AR modeling focuses on parametric spectral estimation rather than explicit transient localization.
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Why is the Morlet wavelet suitable for this analysis?
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How does CWT compare to a short-time Fourier transform (STFT)?