___________________________________ Audio Engineering Society Convention Paper Presented at the 111th Convention 2001 September 21–24 New York, NY, USA This convention paper has been reproduced from the author’s advance manuscript, without editing, corrections, or consideration by the Review Board. The AES takes no responsibility for the contents. Additional papers may be obtained by sending request and remittance to Audio Engineering Society, 60 East 42nd Street, New York, New York 10165-2520, USA; also see www.aes.org . All rights reserved. Reproduction of this paper, or any portion thereof, is not permitted without direct permission from the Journal of the Audio Engineering Society. ___________________________________ Efficient compression of oversampled 1-bit audio signals Reiss, J. D. and Sandler, M. B. Electronic Engineering, King’s College, University of London, Strand, London WC2R 2LS, U.K. josh.reiss@kcl.ac.uk ABSTRACT Sigma delta modulation is a popular technique for high-resolution analog-to-digital conversion and digital-to- analog-conversion. It has been considered as a new format for recording and storage of audio signals. To reduce the storage capacity, a lossless compression scheme can be applied. However, this scheme offers less than 3:1 compression. This may not be sufficient for storage on media such as a Digital Versatile Disk (DVD). We propose a scheme based on a technique known as bit-grouping. Errors are introduced in the compression, but they are confined to frequencies outside the audible range. Our studies indicate that bit-grouping allows one to achieve greater than 4:1 compression. INTRODUCTION Sigma-delta (or delta-sigma) modulation is a popular method for high-resolution A/D and D/A converters. It is frequently used in audio processing and has a wide range of applications. Sigma-delta modulators operate using a trade-off between oversampling and low-resolution quantization. That is, a signal is sampled at much higher than the Nyquist frequency, typically with one bit quantization, so that the signal may be effectively quantized with a resolution on the order of 14-20 bits.[1] Recent work has concentrated on tone suppression[2, 3], multibit modulation[4] and chaotic modulation[5-7]. A new recording format for audio signals, Direct Stream Digital, employing 1-bit oversampling sigma-delta modulation, has recently been proposed and employed as an alternative to the currently widely used multi-bit recording format.[8] The oversampling rate is chosen to be 64 s f ⋅ with 44.1kHz s f = . One of the drawbacks of sigma-delta modulation is the high oversampling rate. This results in a raw (uncompressed) audio data capacity which is typically 4 times as high as that needed for current CD signals. Thus compression becomes essential. However, the theoretical limits on lossless compression of 1-bit sigma delta signals are prohibitive. Fortunately, the signal is intended for audio. Thus only a narrow frequency range needs to be undistorted. This implies that some loss is allowable if it does not degrade the audio. Therefore it might be possible to modify the signal so that a far better compression ratio might be achieved, yet without causing a significant degradation of the output. This is the main focus of this paper. BACKGROUND The simplest, first order sigma-delta modulator consists of a 1-bit quantizer embedded in a negative feedback loop that also contains a discrete-time integrator. The analogue output is sampled at a frequency higher than the Nyquist frequency and is converted into a binary output. The system may be represented by the map[9]