On-line data compression and error analysis using wavelet technology

Wavelet representation of a signal is efficient for process data compression. An on-line compression algorithm based on Haar wavelets is proposed here. As a new data point arrives, the algorithm computes all the approximation coefficients and updates the multiresolution tree before it prepares to receive the next data point An efficient bookkeeping and indexing scheme improves compression ratio more significantly than batch-mode wavelet compression. Reconstruction algorithms and historian format for this bookkeeping are developed. Various analytical results on the bounds on compression ratio and sum of the square error that can be achieved using this algorithm are derived. Experimental evaluation over two sets of plant data shows that wavelet compression is superior to conventional interpolative methods (such as boxcar, backward slope, and SLIM3) in terms of quality of compression measured both in time and frequency domain and that the proposed on-line wavelet compression algorithm performs better than the batch-mode wavelet compression algorithm due to the efficient indexing and bookkeeping scheme. The on-line algorithm combines the high quality of compression of wavelet-based methods and on-line implementation of interpolative compression algorithms at the same time.