A Low Complexity Energy Spreading Transform Coder

Abstract. We have shown how the Prometheus Orthonormal Set (PONS tm ), originally constructed to prove an uncertainty principle conjecture of H. S. Shapiro, can be effectively used to compress all common digital audio signals. This compression method is ef­fective because of two fundamental properties: computational simplicity and energy spreading. Although there exist other transform coding methods, such as Walsh-Hadamard, which give compression while limiting the computational burden, we believe that the energy­spreading feature of PONS is unique. We discuss the various advantages that result from these properties, show how the multidimen­sional analogue of PONS is constructed, and present an algorithm to decompose multidimensional data sets into smaller blocks with uni­formly bounded energy. We then indicate the application of PONS to image processing.