Multiple sets of complicated functional data with sharp changes have appeared in many engineering studies for suchpurposes as monitoring the quality and detecting faults in manufacturing processes. Some of the data curves in thesestudies exhibit large variations in local regions. This paper present a wavelet-based data reduction procedure to reducehigh dimensional functional data from manufacuring processes. The proposed method can characterize the variationsof multiple curves at certain local regions. In addition, unlike existing methods, which is based on a single curve, themethod can handle with multiple curves together for the reduction of high dimensional data having distinct structures. Evaluation with real-life data sets shows that the proposed procedure performs better than several techniques extendedfrom methods based on single-curve-based data reduction.