Efficient Realization of Wave Digital Components for Physical Modeling and Sound Synthesis
01 Jul 2008-IEEE Transactions on Audio, Speech, and Language Processing (IEEE)-Vol. 16, Iss: 5, pp 947-956
TL;DR: Methods to realize consolidated impedance or admittance wave ports that are compatible to WDFs and digital waveguides are explored and attention is paid to simplicity of parametric control.
Abstract: Wave digital filters (WDFs) were originally developed for robust discrete-time simulation of analog filters, but recently they have been applied successfully to modeling of physical systems such as musical instruments and to model-based sound synthesis. While basic WDF elements are sufficient to implement arbitrary passive lumped-element models, the computational efficiency of such models is not optimal. In this paper, we explore methods to realize consolidated impedance or admittance wave ports that are compatible to WDFs and digital waveguides. In addition to efficiency, attention is paid to simplicity of parametric control. A modeling and sound synthesis case study of the bell is presented to demonstrate the performance obtained by the consolidated approach.
Citations
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30 Nov 2015
TL;DR: A novel framework for developing Wave Digital Filter models from reference circuits with multiple/multiport nonlinearities that significantly expands the class of appropriate WDF reference circuits and suggests a derivative of the K-method.
Abstract: We present a novel framework for developing Wave Digital Filter (WDF) models from reference circuits with multiple/multiport nonlinearities. Collecting all nonlinearities into a vector at the root of a WDF tree bypasses the traditional WDF limitation to a single nonlinearity. The resulting system has a complicated scattering relationship between the nonlinearity ports and the ports of the rest of the (linear) circuit, which can be solved by a Modified-NodalAnalysis-derived method. For computability reasons, the scattering and vector nonlinearity must be solved jointly; we suggest a derivative of the K-method. This novel framework significantly expands the class of appropriate WDF reference circuits. A case study on a clipping stage from the Big Muff Pi distortion pedal involves both a transistor and a diode pair. Since it is intractable with standard WDF methods, its successful simulation demonstrates the usefulness of the novel framework.
41 citations
10 Mar 2011
37 citations
TL;DR: Four modified-nodal-analysis-based scattering matrix derivations for non-series/parallel junctions which may absorb linear multiports are presented, using parametric waves with voltage, power, and current waves as particular cases.
Abstract: The wave digital filter (WDF) technique derives digital filters from analog prototypes that classically have been restricted to passive circuits with series/parallel topologies. Since most audio circuits contain active elements (e.g., op-amps) and complex topologies, WDFs have only had limited use in virtual analog modeling. In this paper, we extend the WDF approach to accommodate the unbounded class of non-series/parallel junctions which may absorb linear multiports. We present four modified-nodal-analysis-based scattering matrix derivations for these junctions, using parametric waves with voltage, power, and current waves as particular cases. Three derivations afford implementations whose cost in multiplies are lower than multiplying by the scattering matrix. Negative port resistances may be needed in WDF modeling of active circuits, restricting the WDF to voltage or current waves. We propose two techniques for localizing this restriction. Case studies on the Baxandall tone circuit and a “Frequency Booster” guitar pedal demonstrate the proposed techniques in action.
36 citations
Additional excerpts
...feedback, bridges [24]) that have not been systematized in WDF modeling....
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30 Nov 2015
TL;DR: The class of acceptable reference circuits for WDF modeling is greatly expanded, demonstrated by case studies on circuits which were previously intractable with WDF methods: the Bassman tone stack and Tube Screamer tone/volume stage.
Abstract: We present a Modified-Nodal-Analysis-derived method for developing Wave Digital Filter (WDF) adaptors corresponding to complicated (non-series/parallel) topologies that may include multiport linear elements (e.g. controlled sources and transformers). A second method resolves noncomputable (non-tree-like) arrangements of series/parallel adaptors. As with the familiar 3-port series and parallel adaptors, one port of each derived adaptor may be rendered reflection-free, making it acceptable for inclusion in a standard WDF tree. With these techniques, the class of acceptable reference circuits for WDF modeling is greatly expanded. This is demonstrated by case studies on circuits which were previously intractable with WDF methods: the Bassman tone stack and Tube Screamer tone/volume stage.
28 citations
Cites background or methods from "Efficient Realization of Wave Digit..."
...Until now simulation of this circuit as a WDF would require the use of component consolidation [3] or topological transformations such as the Y –∆ (“wye–delta”) transformation [36]....
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...For instance, bridged-T networks [2] are commonly present in guitar tone stack circuits [3, 4] and analog drum machine circuits [5–7]....
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TL;DR: This paper reviews some of the recent advances in real-time musical effects processing and synthesis, specifically digital emulation of vintage delay and reverberation effects, tube amplifiers, and voltage-controlled filters.
Abstract: This paper reviews some of the recent advances in real-time musical effects processing and synthesis. The main emphasis is on virtual analog modeling, specifically digital emulation of vintage delay and reverberation effects, tube amplifiers, and voltage-controlled filters. Additionally, adaptive effects algorithms and sound synthesis and processing languages are discussed.
25 citations
Cites result from "Efficient Realization of Wave Digit..."
...The simulation is implemented as a computationally efficient fully parametric real-time model using the BlockCompiler software [76], developed by Matti Karjalainen....
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...The consolidation of linear and time-invariant WDF elements as larger blocks for increasing computational efficiency is suggested already in an earlier work by Karjalainen [71]....
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...as larger blocks for increasing computational efficiency is suggested already in an earlier work by Karjalainen [71]....
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References
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Book•
01 Jan 1992TL;DR: This paper presents a meta-analysis of the Z-Transform and its application to the Analysis of LTI Systems, and its properties and applications, as well as some of the algorithms used in this analysis.
Abstract: 1. Introduction. 2. Discrete-Time Signals and Systems. 3. The Z-Transform and Its Application to the Analysis of LTI Systems. 4. Frequency Analysis of Signals and Systems. 5. The Discrete Fourier Transform: Its Properties and Applications. 6. Efficient Computation of the DFT: Fast Fourier Transform Algorithms. 7. Implementation of Discrete-Time Systems. 8. Design of Digital Filters. 9. Sampling and Reconstruction of Signals. 10. Multirate Digital Signal Processing. 11. Linear Prediction and Optimum Linear Filters. 12. Power Spectrum Estimation. Appendix A. Random Signals, Correlation Functions, and Power Spectra. Appendix B. Random Numbers Generators. Appendix C. Tables of Transition Coefficients for the Design of Linear-Phase FIR Filters. Appendix D. List of MATLAB Functions. References and Bibliography. Index.
3,911 citations
"Efficient Realization of Wave Digit..." refers methods in this paper
...…the behavior of a wave port is described by its reflectance (2) Wave digital filters are derived from analog prototypes by the bilinear mapping [20] (3) where is the complex-valued Laplace transform variable with angular frequency , is the sample period, and is the discrete-time…...
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Book•
01 Jan 1991
TL;DR: In this paper, the authors present a survey of the materials for musical instruments and their use in sound generation by Reed and Lip Vibrations, and their application to musical instruments.
Abstract: Part I: Vibrating Systems. Free and Forced Vibrations of Simple Systems. Continuous Systems in One Dimension: Strings and Bars. Two-Dimensional Systems: Membranes, Plates, and Shells. Coupled Vibrating Systems. Nonlinear Systems.- Part II: Sound Waves. Sound Waves in Air. Sound Radiation. Pipes, Horns, and Cavities.- Part III: String Instruments. Guitars and Lutes. Bowed String Instruments. Harps, Harpsicords, Clavicords, and Dulcimers. The Piano.- Part IV: Wind Instruments. Sound generation by Reed and Lip Vibrations. Lip-driven Brass Instruments. Woodwind Reed Instruments. Flutes and Flue Organ Pipes. Pipe Organs.- Part V: Percussion Instruments. Drums. Mallet Percussion Instruments. Cymbals, Gongs, Plates, and Steel Drums. Bells.- Part VI: Materials. Materials for Musical Instruments.- Name Index.- Subject Index.
1,151 citations
TL;DR: This work presents a comprehensive review of FIR and allpass filter design techniques for bandlimited approximation of a fractional digital delay, focusing on simple and efficient methods that are well suited for fast coefficient update or continuous control of the delay value.
Abstract: A fractional delay filter is a device for bandlimited interpolation between samples. It finds applications in numerous fields of signal processing, including communications, array processing, speech processing, and music technology. We present a comprehensive review of FIR and allpass filter design techniques for bandlimited approximation of a fractional digital delay. Emphasis is on simple and efficient methods that are well suited for fast coefficient update or continuous control of the delay value. Various new approaches are proposed and several examples are provided to illustrate the performance of the methods. We also discuss the implementation complexity of the algorithms. We focus on four applications where fractional delay filters are needed: synchronization of digital modems, incommensurate sampling rate conversion, high-resolution pitch prediction, and sound synthesis of musical instruments.
1,014 citations
01 Feb 1986
TL;DR: Wave digital filters (WDFs) as discussed by the authors are modeled after classical filters, preferably in lattice or ladder configurations or generalizations thereof, and have very good properties concerning coefficient accuracy requirements, dynamic range, and especially all aspects of stability under finite-arithmetic conditions.
Abstract: Wave digital filters (WDFs) are modeled after classical filters, preferably in lattice or ladder configurations or generalizations thereof. They have very good properties concerning coefficient accuracy requirements, dynamic range, and especially all aspects of stability under finite-arithmetic conditions. A detailed review of WDF theory is given. For this several goals are set: to offer an introduction for those not familiar with the subject, to stress practical aspects in order to serve as a guide for those wanting to design or apply WDFs, and to give insight into the broad range of aspects of WDF theory and its many relationships with other areas, especially in the signal-processing field. Correspondingly, mathematical analyses are included only if necessary for gaining essential insight, while for all details of more special nature reference is made to existing literature.
937 citations
"Efficient Realization of Wave Digit..." refers background in this paper
...Due to the analogies between physical domains, similar elements can be defined for example for the mechanical and the acoustical domains....
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Journal Article•
686 citations