| Wavelet Transform Adaptive Signal Detection is a signal detection method that uses the Wavelet Transform Adaptive Filter (WTAF). The WTAF is the application of adaptive filtering on the subband signals obtained by wavelet decomposition and reconstruction. The WTAF is an adaptive filtering technique that leads to good convergence and low computational complexity. It can effectively adapt to non-stationary signals, and thus could find practical use for transient signals.; Different architectures for implementing the WTAF were proposed and studied in this dissertation. In terms of the type of the wavelet transform being used, we presented the DWT based WTAF and the wavelet tree based WTAF. In terms of the position of the adaptive filter in the signal paths of the system, we presented the Before-Reconstruction WTAF, in which the adaptive filter is placed before the reconstruction filter; and the After-Reconstruction WTAF, in which the adaptive filter is placed after the reconstruction filter. This could also be considered as implementing the adaptive filtering in different domains, with the Before-Reconstruction structure corresponding to adaptive filtering in the scale-domain, and the After-Reconstruction structure corresponding to adaptive filtering in the time-domain. In terms of the type of the error signal used in the WTAF, we presented the output error based WTAF and the subband error based WTAF. In the output error based WTAF, the output error signal is used as input to the LMS algorithm. In the subband error based WTAF, the error signal in each subband is used as input to the LMS algorithm. The algorithms for the WTAF were also generalized in this work. In order to speed up the calculation, we developed the block LMS based WTAF, which modifies the weights of the adaptive filter block-by-block instead of sample-by-sample.; Experimental studies were performed to study the performance of different implementation schemes for the WTAF. Simulations were performed on different WTAF algorithms with a sinusoidal input and with a pulse input. The speed and stability properties of each structure were studied experimentally and theoretically. It was found that different WTAF structures had different tradeoffs in terms of stability, performance, computational complexity, and convergence speed.; The WTAF algorithms were applied to an online measurement system for fabric compressional behavior and they showed encouraging results. A 3-stage DWT based WTAF and a block WTAF based on a 3-stage DWT was employed to process the noisy force-displacement signal acquired from the online measurement system. The signal-to-noise ratio was greatly increased by applying these WTAFs, which makes a lower sampling rate a possibility. The reduction of the required time for data sampling and processing greatly improves the system speed to meet faster testing requirements. The WTAF algorithm could also be used in other applications requiring fast processing, such as in the real-time applications in communications, measurement, and control. |
