Physically Inspired Models for the Synthesis of Stiff Strings with Dispersive Waveguides
<p/> <p>We review the derivation and design of digital waveguides from physical models of stiff systems, useful for the synthesis of sounds from strings, rods, and similar objects. A transform method approach is proposed to solve the classic fourth-order equations of stiff systems in ord...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2004-01-01
|
| Series: | EURASIP Journal on Advances in Signal Processing |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S1110865704402200 |
| _version_ | 1811293007807250432 |
|---|---|
| author | Testa I Evangelista G Cavaliere S |
| author_facet | Testa I Evangelista G Cavaliere S |
| author_sort | Testa I |
| collection | DOAJ |
| description | <p/> <p>We review the derivation and design of digital waveguides from physical models of stiff systems, useful for the synthesis of sounds from strings, rods, and similar objects. A transform method approach is proposed to solve the classic fourth-order equations of stiff systems in order to reduce it to two second-order equations. By introducing scattering boundary matrices, the eigenfrequencies are determined and their <inline-formula><graphic file="1687-6180-2004-463747-i1.gif"/></inline-formula> dependency is discussed for the clamped, hinged, and intermediate cases. On the basis of the frequency-domain physical model, the numerical discretization is carried out, showing how the insertion of an all-pass delay line generalizes the Karplus-Strong algorithm for the synthesis of ideally flexible vibrating strings. Knowing the physical parameters, the synthesis can proceed using the generalized structure. Another point of view is offered by Laguerre expansions and frequency warping, which are introduced in order to show that a stiff system can be treated as a nonstiff one, provided that the solutions are warped. A method to compute the all-pass chain coefficients and the optimum warping curves from sound samples is discussed. Once the optimum warping characteristic is found, the length of the dispersive delay line to be employed in the simulation is simply determined from the requirement of matching the desired fundamental frequency. The regularization of the dispersion curves by means of optimum unwarping is experimentally evaluated.</p> |
| first_indexed | 2024-04-13T04:54:59Z |
| format | Article |
| id | doaj.art-129965acb0a848feb328f77755d55a67 |
| institution | Directory Open Access Journal |
| issn | 1687-6172 1687-6180 |
| language | English |
| last_indexed | 2024-04-13T04:54:59Z |
| publishDate | 2004-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | EURASIP Journal on Advances in Signal Processing |
| spelling | doaj.art-129965acb0a848feb328f77755d55a672022-12-22T03:01:32ZengSpringerOpenEURASIP Journal on Advances in Signal Processing1687-61721687-61802004-01-0120047463747Physically Inspired Models for the Synthesis of Stiff Strings with Dispersive WaveguidesTesta IEvangelista GCavaliere S<p/> <p>We review the derivation and design of digital waveguides from physical models of stiff systems, useful for the synthesis of sounds from strings, rods, and similar objects. A transform method approach is proposed to solve the classic fourth-order equations of stiff systems in order to reduce it to two second-order equations. By introducing scattering boundary matrices, the eigenfrequencies are determined and their <inline-formula><graphic file="1687-6180-2004-463747-i1.gif"/></inline-formula> dependency is discussed for the clamped, hinged, and intermediate cases. On the basis of the frequency-domain physical model, the numerical discretization is carried out, showing how the insertion of an all-pass delay line generalizes the Karplus-Strong algorithm for the synthesis of ideally flexible vibrating strings. Knowing the physical parameters, the synthesis can proceed using the generalized structure. Another point of view is offered by Laguerre expansions and frequency warping, which are introduced in order to show that a stiff system can be treated as a nonstiff one, provided that the solutions are warped. A method to compute the all-pass chain coefficients and the optimum warping curves from sound samples is discussed. Once the optimum warping characteristic is found, the length of the dispersive delay line to be employed in the simulation is simply determined from the requirement of matching the desired fundamental frequency. The regularization of the dispersion curves by means of optimum unwarping is experimentally evaluated.</p>http://dx.doi.org/10.1155/S1110865704402200physical modelsdispersive waveguidesfrequency warping |
| spellingShingle | Testa I Evangelista G Cavaliere S Physically Inspired Models for the Synthesis of Stiff Strings with Dispersive Waveguides EURASIP Journal on Advances in Signal Processing physical models dispersive waveguides frequency warping |
| title | Physically Inspired Models for the Synthesis of Stiff Strings with Dispersive Waveguides |
| title_full | Physically Inspired Models for the Synthesis of Stiff Strings with Dispersive Waveguides |
| title_fullStr | Physically Inspired Models for the Synthesis of Stiff Strings with Dispersive Waveguides |
| title_full_unstemmed | Physically Inspired Models for the Synthesis of Stiff Strings with Dispersive Waveguides |
| title_short | Physically Inspired Models for the Synthesis of Stiff Strings with Dispersive Waveguides |
| title_sort | physically inspired models for the synthesis of stiff strings with dispersive waveguides |
| topic | physical models dispersive waveguides frequency warping |
| url | http://dx.doi.org/10.1155/S1110865704402200 |
| work_keys_str_mv | AT testai physicallyinspiredmodelsforthesynthesisofstiffstringswithdispersivewaveguides AT evangelistag physicallyinspiredmodelsforthesynthesisofstiffstringswithdispersivewaveguides AT cavalieres physicallyinspiredmodelsforthesynthesisofstiffstringswithdispersivewaveguides |