Spectral analysis of non-stationary signals and applications

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Spectral analysis is one of the most fundamental analysis tools available to scientists. Despite its ubiquity, there are inherent difficulties with this tool. Traditional spectral analysis tools can have difficulty with signals whose spectrum changes quickly with time. A recent major advance in the field of spectral analysis is the Hilbert Huang transform (HHT). This algorithm uses a heuristic algorithm called empirical mode decomposition (EMD), to decompose the signal into sums of 'narrowband' signals for which a good solution to the spectral analysis problem, the Hilbert Transform, exists. Several significant limitations have been identified with the algorithm. It is computationally expensive. The algorithm is not able to separate signals with frequency differences of less than 10%. The algorithm can fail to separate signals with low relative energy. Artifacts are introduced into the signal at the end points. The researcher has developed an alternative means of decomposing that overcomes these limitations. Most significantly, this approach is not computationally more expensive than the fast Fourier transform (FFT), and for signals with sparse spectral components, can be significantly more efficient than the FFT. This approach, however, also presently suffers from limitations. These include a limit on the number of spectral lines that can be present in the signal and the necessity of good initialization of this locally convergent algorithm. The two main goals of this research are to reduce and eliminate the existing limitations of this algorithm as greatly as possible and apply this new approach to applications such as power systems frequency and impedance measurements and resistance measurement in resistance spot welding. The results of this research will be a spectral analysis tool as powerful as the HHT but with much greater frequency separating power, and the computational cost of the FFT. Its application will solve the long standing problem of measuring weld voltage for resistance spot welding of vehicles. This has the potential of increasing the quality and safety of automobiles, of creating savings of millions of dollars per year and giving Canadian manufacturing plants a competitive advantage against international competition.