This paper proposes a novel approach to signal compression (one-dimensional and two-dimensional) using a recently developed multiresolution technique called the Slantlet Transform (ST). The paper outlines the basic principle of ST and suggests an efficient procedure for compression/expansion of the signal using this transform. To compare its performance the DWT compression scheme is also discussed. Exhaustive computer simulation results are carried out on both the techniques for compression and reconstruction operation using standard 1D signals and 2D images. The effect of thresholding and compression potentiality in terms of percentage of retain energy are also assessed. In general, it is observed that the ST is a better candidate for signal compression compared to the DWT based scheme.