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Reference: Wald, R., T. M. Khoshgoftaar, P.-P. Beaujean, and J. C. Sloan, 2010: Combining wavelet and fourier transforms in reliability analysis of ocean systems. Proceedings, 16th International ISSAT on Reliability and Quality in Design, 5-7 August, 2010, International Society of Science and Applied Technologies, 324-328. ISBN: 978-0-9763486-6-5.
Abstract: Frequency spectrum data is encountered in a variety of reliability contexts. In ocean systems, for example, vibration sensors can be used to monitor the state of rotating machinery. Determining when these frequencies have changed, and the nature of these changes, is crucial for fault detection. Traditionally, Fast Fourier Transforms (FFTs) have been used to decompose the input signal into equal-sized frequency bins. Unfortunately, these have difficulty analyzing a wide range of frequencies over different time scales. A newer technique, wavelet transforms, can help overcome these challenges, but lacks some of the frequency resolution of Fourier transforms. This paper discusses how each are used independently, and then provides an approach for using both in tandem to improve responsiveness to changing frequency information. We also introduce a method of performing a wavelet transform on streaming data with a minimum of data storage.