Trend Analysis Using the Frazier-Jawerth Transform
This chapter discusses the Frazier-Jawerth Transform (FJT), a new transform for time-frequency analysis (Frazier and Jawerth, 1985) and a new method for its on-line implementation. Algorithms for FJ decomposition and reconstruction of 1-D signals are also included. FJT bears close resemblance to the wavelet transform technique which is enjoying much attention lately (Science, August 1990). The theory of frames has been shown to subsume the FJ and the wavelet transforms (Heil and Walnut, 1989). It is now widely believed that these new time-frequency techniques may replace the Fourier transform and older time-frequency techniques in some applications in future. Potential applications of interest to chemical engineers include analysis of dynamic systems, process control, solution of partial differential equations, geoexploration data processing, vibration/acoustic testing methods, artificial neural networks etc. FJT has been employed as a time-series data preprocessing mechanism in an artificial neural network based process trend and abnormality detection scheme.
KeywordsAnalyze Function Frequency Domain Discrete Fourier Transform Original Signal Effective Radius
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