Application of approximate trigonometric expansions to multiresolution signal representation

Abstract

Signal representation and data coding for multidimensional signals have received considerable attention due to their importance to several modern technologies. Many useful contributions have been reported that employ wavelets and transform methods. Transform techniques have been generally applied for waveform coding, where constrained representation has been widely used. There is tradeoff between transform efficiency and ease of its implementation and the application depends upon the criterion applicable in any particular case. There exists an approximate Fourier expansion (AFE) with theoretically uncorrelated coefficients. Approximate trigonometric expansions have the capability of fast implementation as well as relatively better decorrelation efficiency than the discrete cosine transform. Some properties of these expansions along with their application to images has already been explored. We apply approximate trigonometric expansions to 1-D signals. Signal decomposition of the signal has been widely used with the discrete cosine transform for signal compression. Here, 1-D signals are decomposed using approximate Fourier expansion (AFE) and later these decomposed signals are represented using an approximate cosine expansion (ACE) for purposes of coding. Computer simulation results are presented.