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v3.1, 20040329, ME

Session K Monday, May 10 09:00 h–12:30 h
(focus on algorithms and equalization)
Chair: Stanley Lipshitz, University of Waterloo, Waterloo, Ontario, Canada

K-1 Signal Processing Techniques for Robust Multichannel Sound EqualizationJohn Sarris, Nick Stefanakis, George Cambourakis, National Technical University of Athens, Athens, Greece
Multichannel equalization is generally accomplished by designing inverse filters to remove the distortion associated with the transmission paths between a set of sources and receivers. The filters are estimated by minimizing a cost function based on the least squares error criterion. However, under certain conditions this least squares error-based formulation fails to provide a solution or provides a solution that lacks robustness. These conditions are investigated and modifications are introduced in the definition of the cost function so that the problem always has a solution with increased robustness. Moreover, the multiple error LMS algorithm is employed to adapt the filter coefficients to their optimum values. Issues like convergence speed and stability are discussed, and simulation results are presented.
K-2 Equalization Methods with True Response Using Discrete FiltersRay Miller, Rane Corp., Mukilteo, WA, USA
Equalizers with fixed frequency filter bands, although successful, have historically had a combined frequency response that at best only roughly matches the band amplitude settings. This situation is explored in practical terms with regard to equalization methods, filter band interference, and desirable frequency resolution. Fixed band equalizers generally use second-order discrete filters. Equalizer band interference can be better understood by analyzing the complex frequency response of these filters and the characteristics of combining topologies. Response correction methods may avoid additional audio processing by adjusting the existing filter settings in order to optimize the response. A method is described which closely approximates a linear band interaction by varying bandwidth, in order to efficiently correct the response.
K-3 Direct Method with Random Optimization for Parametric IIR Audio Equalization. Applications to One Way and Multiway SystemsGermán Ramos, José Javier López, Universidad Politécnica de Valencia, Valencia, Spain
This paper presents a novel method for audio equalization using IIR (Infinite Impulse Response) filters. The algorithm is based on a direct method with a random parametric optimization process using second- order sections (RaPOSOS). Given a loudspeaker response, and the definition of the desired electroacoustical target response, an optimized filter is obtained. For full band loudspeakers, a bank of peak filters is designed to perform the equalization. For multiway systems, the process is repeated for each way with bandpass targets using lowpass, highpass, and peak filters computing the combined response and performing time-align correction. The final result provides the parameters that define each filter (frequency, gain, Q) in correct order of importance; first the ones that perform deepest improvement, so that scalable solutions with different degrees of correction could be derived.
K-4 Performance Improvements for Audio Algorithms that Use Nonsequential Memory Accesses on Digital Signal Processors— Matthew Watson1, Vineet Ganju1, Gaganjot Maur2
Texas Instruments, Inc., Stafford, TX, USA
Texas Instruments (India) Pvt. Ltd., Bangalore, India
Many audio algorithms, such as room simulators and reverberators, operating on digital signal processors access large delay buffers in a nonsequential fashion. Generally, these delay buffers are too large to reside in the on-chip memory of the processor, so they must be placed in external, slow memories. Furthermore, the nonsequential accesses present a problem for maintaining high performance. This paper presents a number of methods that may be employed to improve the performance of the memory accesses of such algorithms. Methods examined include the use of direct CPU memory access, hardware data cache, and dedicated direct memory access (DMA) controllers. Additionally, the type of algorithm, delay taps, and sample block size will be examined and performance results will be presented.
K-5 Method for Estimating Magnitude and Phase in the MDCT Domain—Corey Cheng, Dolby Laboratories, San Francisco, CA, USA
This paper introduces a method for estimating the magnitude and phase responses in audio coders that employ the Modified Discrete Cosine Transform (MDCT). This technique computes magnitude and phase estimates at the decoder using two pieces of information: (1) MDCT coefficients transmitted by the encoder; (2) an estimate of the Modified Discrete Sine Transform (MDST) computed from the transmitted MDCT coefficients. In this manner, approximate magnitude and phase estimates suitable for use with some decoder-oriented signal processing techniques can be constructed entirely from MDCT coefficients available at the decoder. We show that these approximate methods are less computationally intensive than exact methods, and we compare the performance of the approximate methods to exact methods.
K-6 The Harmonic Content of a Limit Cycle in a DSD BitstreamJoshua Reiss, Mark Sandler, Queen Mary, University of London, London, UK
This paper explores the effects of limit cycles on the frequency content in the DSD bitstream. We show how any periodic bitstream can be expressed as a sum of square waves of various phases with width equal to the sampling period. A Fourier expansion may be used to exactly determine the phases and amplitudes of all spectral content. We thus determine all harmonics that appear in the output, and through the comparison with psychoacoustic models, determine the audibility of limit cycles. These results are verified through the simulation of realistic high-order sigma-delta modulators, and put into the context of recent advances in the theory of limit cycles and idle tones in sigma delta modulators.
K-7 Toward a Better Understanding of 1-Bit Sigma-Delta Modulators—Part 4— John Vanderkooy, Stanley Lipshitz, University of Waterloo, Waterloo, Ontario, Canada
This is Part 4 of an ongoing investigation into the behavior of 1-bit sigma-delta modulators. In this paper we question the usual concept of the “average quantizer gain” as it applies to the quantizer transfer characteristic and the stability of a 1-bit modulator. We show that the concept is very poorly defined and of little use for understanding the operation of the 1-bit modulator. We also investigate a number of possible alternative definitions of the gain, and their significance.

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