A signal consists of multiple components occurring at different frequencies. Current analysis methods analyze signals either in time or frequency domain but not in both at the same time. Time series analysis is major topic in signal processing. Any control engineer spends endless nights studying the Fourier transformations which convert a time series into the frequency domain and you can draw fancy graphs and shape your frequency response of your controller. These methods work very nicely for linear systems, meaning if you can open a valve infinitely :).
I am interested in analyzing signals in both domains at the same time. This would enable the use of methodologies from both domains, like constrains and events in time, and data smoothing (multiband frequency filters). Wavelets provide a nice framework for this type of research.
I currently work on simple multiscale threshholding algorithms. The idea and underlying math is extremely simple:
- Convert the signal into multiscale domain using Haar wavelets (http://cnx.rice.edu/content/m10764/latest/)
- Threshold the difference components (i.e. if less then epsilon set it to zero)
- Reconstruct the signal
- Use a moving window for the threshholding algorithm to get multiple reconstructed values for the same data points
- Analyze these points for variance
- Establish an event detection algorithm
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