SNR analysis of log companding for use in a digital recording/data analysis system

This paper presents an SNR analysis of a bilateral log compandor that was used in a portable wide-bandwidth digital recording system designed to generate field recordings of wide-band atmospheric noise in the MF radio spectrum [1], [2]. Log-compression amplifiers are used in the I and Q channels of the recorder receiver function to compress dynamic range from 120 to about 50 dB. Following A/D conversion, the compressed I and Q channel signals are digitally recorded on magnetic tape. The recorded data are then transcribed onto magnetic computer tape for subsequent data analysis. Inverse log compression of the transcribed samples is accomplished via a software log-expansion algorithm exactly matched to the inverse characteristics of each of the I and Q channel log-compression amplifiers. The present analysis shows that samples of the I and Q channel signals can be generated from samples of the log-compressed signals by inverse log compression without concern for aliasing error. A measure of the accuracy of the resulting sampled sequence is then developed analytically in closed form in terms of an SNR measure for the decompressed samples.