This paper aims to extract characteristics of the spectrum of fingerprint image and to apply them to image enhancement techniques in spatial frequency domain. Based on 1$ imes$64 window as a processing unit and the different record lengths(32, 16, 8), the estimate of power spectrum density for each length was made. Each acquired spectrum characteristics was applied to the re-synthesis process of the fingerprint image, an improved gray scale image was obtained. In order to select an optimal predictor and the Huffman table for the fingerprint iamge, the lossless JPEG algorithm was used. Experiments were performed for extracting distribution characteristics for the each of 7 predictors from the fingerprint image and modeling processes, and the result was applied to the data compression algorithm and the selection of the optimal predictor.