Dynamical Systems for Audio Synthesis: Embracing Nonlinearities and Delay-Free Loops

Medine, David

doi:10.3390/app6050134

Cited by 4 publications

(3 citation statements)

References 14 publications

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“…Numerical differentiation of discrete audio data finds numerous applications in solving ordinary and partial differential equations (ODEs and PDEs) as a numerical framework for modeling nonlinear audio circuit systems. It is used, for example, in audio synthesis and creating audio effects [75][76][77][78][79] and music recognition and classification [34,[80][81][82]. It is specifically used for time-frequency analysis based on nonstationary audio signal decomposition (methods derived from empirical mode decomposition [83][84][85][86][87]), enhancement of spectral precision in Fourierbased methods [85,[88][89][90][91], audio steganalysis [92], digital audio authentication [93][94][95], acoustic event detection [96][97][98][99], feature extraction based on Mel-frequency cepstral coefficients (MFCC) [100][101][102][103][104][105][106][107][108], speaker and speech identification and recognition, and sound source tracking [107,[109][110][111][112][113]…”

Section: Numerical Differentiation Of Discrete Audio Datamentioning

confidence: 99%

Estimating the first and second derivatives of discrete audio data

Lewandowski

2024

J AUDIO SPEECH MUSIC PROC.

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A new method for estimating the first and second derivatives of discrete audio signals intended to achieve higher computational precision in analyzing the performance and characteristics of digital audio systems is presented. The method could find numerous applications in modeling nonlinear audio circuit systems, e.g., for audio synthesis and creating audio effects, music recognition and classification, time-frequency analysis based on nonstationary audio signal decomposition, audio steganalysis and digital audio authentication or audio feature extraction methods. The proposed algorithm employs the ordinary 7 point-stencil central-difference formulas with improvements that minimize the round-off and truncation errors. This is achieved by treating the step size of numerical differentiation as a regularization parameter, which acts as a decision threshold in all calculations. This approach requires shifting discrete audio data by fractions of the initial sample rate, which was obtained by fractional delay FIR filters designed with modified 11-term cosine-sum windows for interpolation and shifting of audio signals. The maximum relative error in estimating first and second derivatives of discrete audio signals are respectively in order of $$10^{-13}$$ 10 - 13 and $$10^{-10}$$ 10 - 10 over the entire audio band, which is close to double-precision floating-point accuracy for the first and better than single-precision floating-point accuracy for the second derivative estimation. Numerical testing showed that this performance of the proposed method is not influenced by the type of signal being differentiated (either stationary or nonstationary), and provides better results than other known differentiation methods, in the audio band up to 21 kHz.

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Section: Numerical Differentiation Of Discrete Audio Datamentioning

confidence: 99%

Estimating the first and second derivatives of discrete audio data

Lewandowski

2024

J AUDIO SPEECH MUSIC PROC.

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“…We now consider one interesting way to approximate continuous-time processes in a computer, using numerical differential equation solvers instead of sampled processes. In this discussion I'll rely heavily on work by recent UCSD PhD graduates Andrew Allen [1] and David Medine [5].…”

Section: Example: Modeling the Moog Ladder Filtermentioning

confidence: 99%

ICMC 2015 Keynote Address

Puckette¹

2020

array

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“…Only the single memoryless nonlinearity has been discussed here. A logical extension will be to multiple such nonlinearities in a feedback setting, as it is currently one of the main applications of virtual analog modeling in audio [35], [36], [37], [38], [12]. A major new consideration will be the determination of numerical stability conditions for such antialiasing methods, and will form the basis for future investigations.…”

Section: Conclusion and Further Workmentioning

confidence: 99%

Antiderivative Antialiasing for Memoryless Nonlinearities

Bilbao

Esqueda

Parker

et al. 2017

IEEE Signal Process. Lett.

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Aliasing is a commonly-encountered problem in audio signal processing, particularly when memoryless nonlinearities are simulated in discrete time. A conventional remedy is to operate at an oversampled rate. A new aliasing reduction method is proposed here for discrete-time memoryless nonlinearities, which is suitable for operation at reduced oversampling rates. The method employs higher order antiderivatives of the nonlinear function used. The first order form of the new method is equivalent to a technique proposed recently by Parker et al. Higher order extensions offer considerable improvement over the first antiderivative method, in terms of the signal-to-noise ratio. The proposed methods can be implemented with fewer operations than oversampling and are applicable to discrete-time modeling of a wide range of nonlinear analog systems.

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Dynamical Systems for Audio Synthesis: Embracing Nonlinearities and Delay-Free Loops

Cited by 4 publications

References 14 publications

Estimating the first and second derivatives of discrete audio data

Estimating the first and second derivatives of discrete audio data

ICMC 2015 Keynote Address

Antiderivative Antialiasing for Memoryless Nonlinearities

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