We discuss smooth local trigonometric bases and their applications to signal compression. In image compression, these bases can
reduce the blocking effect that occurs in the Joint Photographic Experts Group (JPEG). We present and compare two generalizations of the original construction of Malvar, Coifman, and Meyer: biorthogonal and equal parity bases. These have the advantage that constant and linear components, respectively, can be represented efficiently. We show how they reduce blocking effects and improve the SNR.