AES Journal

Journal of the AES

2022 June - Volume 70 Number 6

Guest Editor's Note: Special Issue on Audio Filter Design

Authors: Bank, Balázs; Fontana, Federico; Smith, Julius O.

Page: 412

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Review Articles

Warped, Kautz, and Fixed-Pole Parallel Filters: A Review

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In audio signal processing, the aim is the best possible sound quality for a given computational complexity. For this, taking into account the logarithmic frequency resolution of hearing is a good starting point. The present paper provides an overview on warped, Kautz, and fixed-pole parallel filters and demonstrates that they are all capable of achieving logarithmiclike frequency resolution, providing much more efficient filtering or equalization compared to straightforward finite impulse response (FIR) or infinite impulse response (IIR) filters. Besides presenting the historical development of the three methods, the paper discusses their relations and provides a comparison in terms of accuracy, computational requirements, and design complexity. The comparison includes loudspeaker--room response modeling and equalization examples.

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Papers

Linear-Phase Octave Graphic Equalizer

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A computationally efficient octave-band graphic equalizer having a linear-phase response is introduced. The linear-phase graphic equalizer is useful in audio applications in which phase distortion is not tolerated, such as in multichannel equalization, parallel processing, phase compatibility of audio equipment, and crossover network design. The structure is based on the interpolated finite impulse response (IFIR) philosophy. The proposed octave-band graphic equalizer uses one prototype low-pass filter, which is a half-band FIR filter designed using the window method. Stretched versions of the prototype filter and its complementary high-pass filter implement all ten band filters needed. The graphic equalizer is realized in the parallel form, in which the outputs of all band filters, scaled with their individual command gain, are added to compute the equalized output signal. The command gains can be used directly as filter band gains. The number of operations needed per sample is only slightly more than that needed for the graphic equalizer based on minimum-phase recursive filters. A comparison with other implementation approaches demonstrates that the proposed structure requires 99% fewer operations than a high-order FIR filter. The proposed filter uses 39% fewer operations per sample than the fast Fourier transform--based filtering method and causes over 78% less latency.

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Improving the Chamberlin Digital State Variable Filter

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The state variable filter configuration is a classic analog design that has been employed in many electronic music applications. A digital implementation of this filter was put forward by Chamberlin, which has been deployed in both software and hardware forms. Although this has proven to be a straightforward and successful digital filter design, it suffers from some issues, which have already been identified in the literature. From a modified Chamberlin block diagram, we derive the transfer functions describing its three basic responses, highpass, bandpass, and lowpass. An analysis of these leads to the development of an improvement, which attempts to better shape the filter spectrum. From these new transfer functions, a set of filter equations is developed. Finally, the approach is compared with an alternative timedomain--based reorganization of update equations, which is shown to deliver a similar result.

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Real-Time Transient Reduction in Higher-Order Time-Varying Musical Filters

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This paper introduces higher-order digital equalization filters designed using various transforms on lower-order filter prototypes. The filters are designed in the analog domain as state-space filters. The bilinear transform is applied in real time as a trapezoidal integrator on the state equations to discretize the filters while still retaining the time-varying stability properties of the analog prototypes. It is demonstrated that factoring the higher-order filters into second-order sections before discretization introduces transient distortion in time-varying situations; the filters are then designed and implemented as fourth-order sections in the state domain with interpolation because it is more efficient to maintain filter stability and bounding at the higher order in the same time-varying conditions.

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Parallel Wave Digital Filter Implementations of Audio Circuits with Multiple Nonlinearities

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Modern audio systems and musical effects feature multicore processing units. Thus, the development of parallel audio processing algorithms capable of exploiting the architecture of such hardware is in order. In this paper, a parallel version of the hierarchical scattering iterative method (HSIM), a technique based on wave digital filter principles recently proposed for the emulation of multiphysics audio circuits containing multiple nonlinear one-ports and nonlinear transformers, is presented. HSIM operates in a modular fashion, and it is characterized by a high number of embarrassingly parallelizable operations, making it a good candidate for parallel execution. After analyzing HSIM from the parallel computing perspective, three different strategies for the distribution of HSIM workload among threads of execution are proposed, showing how to compute the maximum achievable speedup. The emulation of a possible output stage of a vacuum-tube guitar amplifier is considered, and a performance comparison between parallel and serial implementations of HSIM is presented, pointing out a speedup of nearly 30%. The proposed method thus proves to be promising for virtual analog modeling applications, leading the way towards the parallel digital emulation of increasingly complex audio circuits.

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Audio Peak Reduction Using Ultra-Short Chirps

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Two filtering methods for reducing the peak value of audio signals are studied. Both methods essentially warp the signal phase while leaving its magnitude spectrum unchanged. The first technique, originally proposed by Lynch in 1988, consists of a wideband linear chirp. The listening test presented here shows that the chirp must not be longer than 4 ms, so as not to cause any audible change in timbre. The second method, called the phase rotator, put forward in 2001 by Orban and Foti is based on a cascade of second-order all-pass filters. This work proposes extensions to improve the performance of the methods, including rules to choose the parameter values. A comparison with previous methods in terms of achieved peak reduction, using a collection of short audio signals, is presented. The computational load of both methods is sufficiently low for real-time application. The extended phase rotator method is found to be superior to the linear chirp method and comparable to the other search methods. The practical peak reduction obtained with the proposed methods spans from 0 to about 3.5 dB. The signal processing methods presented in this work can increase loudness or save power in audio playback.

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A Workflow and Digital Filters for Correcting Speed and Equalization Errors on Digitized Audio Open-Reel Magnetic Tapes

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This paper presents a workflow and digital filters for compensating speed and equalization errors that can impact digitized audio open-reel tapes. Thirty cases of mismatch between recording and reproducing speed (3.75, 7.5, 15, and 30 in/s) and equalization standards [National Association of Broadcasters (NAB), Consultative Committee for International Radio (CCIR), and Audio Engineering Society] were considered. For three frequent cases of mismatch (NAB 3.75 in/s---CCIR 7.5 in/s; NAB 3.75 in/s---CCIR 15 in/s; and NAB 7.5 in/s---CCIR 15 in/s), MUltiple Stimuli with Hidden Reference and Anchor--inspired tests with =21 participants assessed the workflow and digital filters, using excerpts of music and voice. Two different correction filters were used, both of which provided promising results. Following this, subsequent analyses examined predictive variables for correct and incorrect MUltiple Stimuli with Hidden Reference and Anchor performance, as well as spectral and numerical differences between filters, which provide key insights and recommendations for further related work.

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Cylindrical Radial Filter Design With Application to Local Wave Field Synthesis

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The cylindrical radial filters refer to the discrete-time realizations of the radially dependent parts in cylindrical harmonic expansions, which are commonly described by the cylindrical Bessel functions. An efficient and accurate design of the radial filters is crucial in spatial signal processing applications, such as sound field synthesis and active noise control. This paper presents a radial filter design method where the filter coefficients are analytically derived from the time-domain representations. Time-domain sampling of the cylindrical radial functions typically leads to spectral aliasing artifacts and degrades the accuracy of the filter, which is mainly attributed to the unbounded discontinuities exhibited by the time-domain radial functions. This problem is coped with by exploiting an approximation where the cylindrical radial function is represented as a weighted sum of the radial functions in spherical harmonic expansions. Although the spherical radial functions also exhibit discontinuities in the time domain, the amplitude remains finite,which allows application of a recently introduced aliasing reduction method. The proposed cylindrical radial filter is thus designed by linearly combining the spherical radial filters with improved accuracy. The performance of the proposed cylindrical radial filters is demonstrated by examining the spectral deviations from the original spectrum.

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Resynthesis of Spatial Room Impulse Response Tails With Anisotropic Multi-Slope Decays

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Spatial room impulse responses (SRIRs) capture room acoustics with directional information. SRIRs measured in coupled rooms and spaces with non-uniform absorption distribution may exhibit anisotropic reverberation decays and multiple decay slopes. However, noisy measurements with low signal-to-noise ratios pose issues in analysis and reproduction in practice. This paper presents a method for resynthesis of the late decay of anisotropic SRIRs, effectively removing noise from SRIR measurements. The method accounts for both multi-slope decays and directional reverberation. A spherical filter bank extracts directionally constrained signals from Ambisonic input, which are then analyzed and parameterized in terms of multiple exponential decays and a noise floor. The noisy late reverberation is then resynthesized from the estimated parameters using modal synthesis, and the restored SRIR is reconstructed as Ambisonic signals. The method is evaluated both numerically and perceptually, which shows that SRIRs can be denoised with minimal error as long as parts of the decay slope are above the noise level, with signal-to-noise ratios as low as 40 dB in the presented experiment. The method can be used to increase the perceived spatial audio quality of noise-impaired SRIRs.

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Standards and Information Documents

AES Standards Committee News

Page: 540

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Departments

Obituraries

Page: 542

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Book Reviews

Page: 543

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Conv&Conf

Page: 544

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Extras

Table of Contents

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Cover & Sustaining Members List

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AES Officers, Committees, Offices & Journal Staff

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AES - Audio Engineering Society