Logarithmic Compression of Digitally Telemetered Data

To express a number using true logarithmic compression, at least B = log2 [log R log(1 + Q/100 1 - Q/100/)] bits are required. (R = dynamic range, Q = ±error percent.) True logarithmic compression is rarely used in practice, but quasi-logarithmic methods such as normalized floating-point format are used frequently. A partially unnormalized floating-point format provides the best performance in the case of digital data. For this method B = log2 [100 log2 (4R Q/l00 Q 1 - Q/100)]-1. This paper contains analytical and graphical results that facilitate comparison of the various systems.