Discrete Wavelet Methods for Interference Mitigation: An Application To Radio Astronomy

Master Thesis


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The field of wavelets concerns the analysis and alteration of signals at various resolutions. This is achieved through the use of analysis functions which are referred to as wavelets. A wavelet is a signal defined for some brief period of time that contains oscillatory characteristics. Generally, wavelets are intentionally designed to posses particular qualities relevant to a particular signal processing application. This research project makes use of wavelets to mitigate interference, and documents how wavelets are effective in the suppression of Radio Frequency Interference (RFI) in the context of radio astronomy. This study begins with the design of a library of smooth orthogonal wavelets well suited to interference suppression. This is achieved through the use of a multi-parameter optimization applied to a trigonometric parameterization of wavelet filters used for the implementation of the Discrete Wavelet Transform (DWT). This is followed by the design of a simplified wavelet interference suppression system, from which measures of performance and suitability are considered. It is shown that optimal performance metrics for the suppression system are that of Shannon’s entropy, Root Mean Square Error (RMSE) and normality testing using the Lilliefors test. From the application of these heuristics, the optimal thresholding mechanism was found to be the universal adaptive threshold and entropy based measures were found to be optimal for matching wavelets to interference. This in turn resulted in the implementation of the wavelet suppression system, which consisted of a bank of matched filters used to determine which interference source is present in a sampled time domain vector. From this, the astronomy based application was documented and results were obtained. It is shown that the wavelet based interference suppression system outperforms existing flagging techniques. This is achieved by considering measures of the number of sources within a radio-image of the Messier 83 (M83) galaxy and the power of the main source in the image. It is shown that designed system results in an increase of 27% in the number of sources in the recovered radio image and a 1.9% loss of power of the main source.