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

Abstract

This paper presents an SNR analysis of a bilateral log compandor that was used in a portable wide-bandwidth digital re cording 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 / and Q channels of the recorder receiver function to compress dynamic range from 120 to about 50 dB. Fol lowing A/D conversion, the compressed / 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 / and Q channel log-compression am plifiers.The present analysis shows that samples of the / 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. INTRODUCTION T HIS PAPER presents an SNR analysis of bipolar log companding [3] to control dynamic range in a digital recording/data analysis system. While other analyses of this type have been presented previously [4]-[8], the present analysis, in addition to providing a closed-form analytical so lution for the overall compandor SNR, demonstrates a useful result in the application of nonlinear no-memory processing of analog band-limited signals prior to A/D conversion.Specifically, it is shown that a sampled representation of the unprocessed analog signal can be generated from samples of the log-compressed signal (to within a specified level of quantization accuracy) by inverse log compression without concern for aliasing error. Briefly, the system being considered here consists of an analog bipolar log-compression amplifier followed by an A/D converter and high-speed digital tape recorder. The digitally recorded samples are transcribed onto magnetic (computer) tape for subsequent analysis. Logarithmic expansion of the sampled data is applied via an inverse software ^-"décom pression" algorithm prior to data analysis. This algorithm is assumed to be an exact match to the inverse characteristic of the analog log-compression amplifier.The thrust of this paper is to present an SNR analysis of the overall log-companding process that takes place in each / and Q channel between a receiver LPF (low-pass filter) output and the output of the inverse software log-compression algorithm that provides the Ik and Qk samples used in the subsequent data analysis operations.In the present analysis, the total dynamic range of the in stantaneous signal range into the log compressor is assumed to be 120 dB. The upper 90 dB of this range falls in the loga rithmic portion of the log compressor resulting in an effective compression from 90 dB to approximately 21 dB for this range. The lower 30 dB o...