Compressed fixed-point data formats with non-standard compression factors

Sign bit compression in fixed-point numbering systems can improve the dynamic range and round-off noise for signal processing algorithms. This paper analyses non-standard compression factors (CF) for compressed fixed-point data formats, where sign bit compression is performed on each individual fixed-point number. Although these compression techniques are applicable to other fixed-point formats, the compressed two's complement data format is selected for illustration. A brief background on compressed two's complement is provided. Obvious compression factors are powers of two due to binary formatting, but compression factors other than standard powers of two are presented. Compression factors of 3 and 5 are analysed in greater detail. Motivation for and advantages of non-power-of-two compression factors are identified.