A new signal compression scheme is proposed. It is based on all pass extraction from the received signal's transfer function. The all pass parameters are closely related to a linear prediction polynomial LP of the same order, of the received data. Results have shown that, this new algorithm yields far smaller signal's reconstruction errors when compared with other known methods, for the same compression ratio CR. This algorithm is used in image compression and coding, as follows: First, the image is segmented into blocks and the 2-D DCT of each block, is computed. Next, each 2-D DCT matrix is zigzag scanned to yield a 1-D vector, which is subsequently compressed using the proposed scheme. The image is reconstructed in a reverse manner, using the compressed vectors. The image's compressed parameters is further compressed using schemes like EZW or SPHIT coders. Simulation results have revealed that the proposed compression scheme competes very well with JPEG compression schemes, especially when the images have many details.