v7.1, 20040930, me
Saturday, October 30, 1:30 pm 5:00 pm
Session N SIGNAL PROCESSING, Part 2
Chair: Bob Adams, Analog Devices, Norwood, MA, USA
N-1 Moores Law and Digital AudioWhat Have We Done with All the Transistors?Peter Eastty, Pro-Audio Lab, Sony, Oxford, UK
This paper investigates what has happened to the many transistors used in digital audio engineering. Improvements in signal quality have certainly accrued but advances in ease of use, reliability, availability, serviceability, power consumption, delay and cost have far outweighed, from a practical standpoint, advances in audio quality. Many examples are given, a novel signal visualization technique is described, and based upon thehistory some predictions are made.
Convention Paper 6278
N-2 Dither Myths and FactsStanley Lipshitz, John Vanderkooy, University of Waterloo, Waterloo, Ontario, Canada
Twenty-five years after the discovery of the desirable attributes of nonsubtractive triangular probability density function dither for signal quantization, some misunderstandings, myths, and half-truths still abound regarding what dither does and does not do. The increased use of dithered sigma-delta modulators has recently brought some of these questions to the fore. Some of these errors are relatively easy to explain and correct, while others are considerably more subtle in nature, but nevertheless also need to be addressed. This paper attempts to explain and clarify these matters, with the aid of copious time-domain, frequency-domain, and statistical-domain illustrations. It assumes that the reader already has a good knowledge of the theory of dithered quantization.
Convention Paper 6279
N-3 Description of Limit Cycles in Feedback Sigma Delta Modulators Derk Reefman, Philips Research, Eindhoven, The Netherlands; Joshua Reiss, Queen Mary, University of London, London, UK; Erwin Janssen, Philips Research, Eindhoven, The Netherlands; Mark Sandler, Queen Mary, University of London, London, UK
The authors have recently developed a framework for analysis of limit cycle behavior in feedforward sigma delta modulators (SDMs). However, the dynamics of feedback SDMs appear to be completely different. Here, we extend that framework to include limit cycles in feedback SDMs. We prove that for DC inputs, periodic output implies state space periodicity. An outcome of this is that for an Nth order SDM, at least N-1 initial conditions must be fixed in order to have limit cycle behavior. We present expressions for the minimum disturbance of the input or initial conditions that is needed to break up a limit cycle. These expressions are notably different from the analogous expressions for feedforward SDMs. We show that dithering the quantizer is a sub-optimal approach to removing limit cycles, and limit cycle stability is determined. Examples are provided that illustrate the theoretical results, and these results are also compared with those found for feedforward SDM designs. It is shown that, with respect to limit cycle behavior, it makes little difference whether feedforward or feedback designs are used.
Convention Paper 6280
N-4 Implementation of Tree and Stack Algorithms for Look-Ahead Sigma Delta ModulatorsJames Angus, University of Salford, Salford, UK
Look-ahead Sigma-Delta modulators look forward k samples before deciding to output a one or a zero. The Viterbi algorithm is then used to search the trellis of the exponential number of possibilities that such a procedure generates. This paper describes alternative tree-based algorithms. Tree-based algorithms are simpler to implement because they do not require backtracking to determine the correct output value. They can also be made more efficient using Stack algorithms. Both the tree algorithm and the more computationally efficient stack algorithms are described. Implementations of both algorithms are described in some detail. In particular, the appropriate data structures for both the trial filters and score memories.
Convention Paper 6281
N-5 Novel Subwoofer Signal Conditioner Design Using a Fully Programmable Analog Array and Software Tools Ian Macbeth, Anadigm Ltd., Crewe, UK ; Tegid Roberts, Cadarn Consulting Ltd., Eynsham, UK
The control and real-time software programmability of low-frequency audio signals in the analog domain is inaccurate, cumbersome, and expensive. In the digital domain there are issues relating to low frequency distortions, latency, and design time. A fully programmable analog array IC methodology is presented that combines the benefits of DSP programmability with analog signal processing by way of a case study demonstrating software design tools and custom software configuration models. This single-chip subwoofer conditioner solution implements a subsonic filter, adjustable audio compressor, Linkwitz transform filter, and low-pass output filter with full software control. Performance measurements of this implementation, as well as further enhancements to the software models, are also discussed.
Convention Paper 6282
N-6 Characterization of Spherical Loudspeaker ArraysPeter Kassakian, David Wessel, University of California, Berkeley, CA, USA
The synthesis and rotational control of radiation patterns produced by spherical arrays of loudspeakers is studied. We identify operating regions, in terms of complexity of patterns and frequency ranges, over which patterns can be accurately synthesized. By considering an inner product space of far-field patterns, we can reason geometrically about approximation errors when using the systems to synthesize and control target responses. Bounds for normalized error across subspaces, in particular subspaces corresponding to the control operation of rotation, are calculated using singular value decomposition. The bounds can be interpreted as the best and worst case errors encountered when dynamically steering the patterns.
Convention Paper 6283
N-7 Interpolating Linear- and Log-Sampled ConvolutionD. B. (Don) Keele, Jr., Harman International, Northridge, CA, USA
This paper describes a class of FIR filter/convolvers based on interpolation that allow sparse specification of the filters impulse-response waveform or equivalently its frequency spectrum in both linear- and log-spaced domains. Interpolation allows the filters impulse response or frequency response to be specified in significantly fewer samples. This is turn means that far fewer filter taps are required. Linear- and log-sampled interpolating filter/convolvers can further be categorized into two types: Type 1, interpolation in time, and Type 2, interpolation in frequency. Type 1 provides direct specification of the filters impulse response in linear or log time, while Type 2 allows direct specification of the complex (real-imaginary) frequency response of the filter in linear or log frequency. Each form of filter vastly reduces the number of filter taps but greatly increases the processing complexity at each tap. Efficient implementations of the log-spaced filter-convolvers are presented that use multiple asynchronous sample-rate converters. This paper is a continuation of the authors Log Sampling paper presented to the AES in Nov. 1994 [AES 97th Convention, Preprint 3935]. This paper represents work in progress with a conceptual description of the convolution technique with minimal mathematical development.
Convention Paper 6284