A Novel Multi-Exponential Function-based Companding Technique for Uniform Signal Compression over Channels with Limited Dynamic Range

Companding, as a variant of audio level compression, can help reduce the dynamic range of an audio signal. In analog (digital) systems, this can increase the signal-to-noise ratio (signal to quantization noise ratio) achieved during transmission. The µ-law algorithm that is primarily used in the digital telecommunication systems of North America and Japan, adapts a companding scheme that can expand small signals and compress large signals especially at the presence of high peak signals. In this paper, we present a novel multi-exponential companding function that can achieve more uniform compression on both large and small signals so that the relative signal strength over the time is preserved. That is, although larger signals may get considerably compressed, unlike µ-law algorithm, it is guaranteed that these signals after companding will definitely not be smaller than expanded signals that were originally small. Performance of the proposed algorithm is compared with µ-law using real audio signal, and results show that the proposed companding algorithm can achieve much smaller quantization errors with a modest increase in computation time.