Transform with no Parameters Based on Extrema Points for Non-stationary Signal Analysis

Signal transforms are very important tools to extract useful information from scientific, engineering, or medical raw data. Unfortunately, traditional transform techniques impose unrealistic assumptions on the signal, often producing erroneous interpretation of results. Well-known integral transforms, such as short-time Fourier transform, though have fast implementation algorithms (e.g., FFT), are still computationally expensive. They have multiple parameters that should be tuned, and it is not readily clear how to tune them for long-duration non-stationary signals. To solve these problems, one needs a computationally inexpensive transform with no parameters that will highlight important data aspects. We propose a simple transform based on extrema points of the signal. The transform value at a given point is calculated based on the distance and magnitude difference of two extrema points it lies between, rather than considering every point around it. We discuss implementation of the developed algorithm and show examples of successfully applying the transform to noise-corrupted synthetic signals and to sleep studies detecting delta wave in brain EEG signal. Ideas for improvement and further research are discussed.