How can you describe the continuous wavelet transform?
Vibration signal during start-up or shut-down are non-stationary in nature, whcih means the frequency changes with time. The traditional signal procesessing techquique, Fast Fourier Transform (FFT) assumes the signal is stationary and gives the frequency content of the signal whcih prevail at the entire duration of the signal. This property makes the fourior transform unsuitable for analysing the nonstationary vibration signal. Whereas the wavelet transform breaks the signal into its scaled shifted versions of the mother wavelet and hence provides the time-frequency information of a signal, enabling the extraction of features that vary in time. This property of wavelets has been used in the present study to analyze transient or nonstationary signals and also to extract the crack features while the rotor-bearing system deccellerating through the critical speed during shut down.
The continuous wavelet transform (CWT) of a time signal f (t) can be defined as the sum over all time of the signal multiplied by scaled, shifted versions of the wavelet function (t).
Where (t) denotes the mother wavelet. The parameters s and b represent the scale index which is reciprocal of frequency and the time shifting (or translation).”
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