Abstracts (Times New Roman, 12 pt., not exceeding two pages) and c.v. (Times New Roman, 12 pt., not exceeding 1 page) may be submitted to the scientific secretary
deadline abstract invoice: February 28, 2011
abstract acceptation will be communicated after March 15, 2011
Structural, chemical and mechanical imaging applied to the conservation of musical instruments J.-P. Echard1*, S. Le Conte, S. Vaiedelich
laboratoire de recherche et de restauration du Musée de la musique - Cité de la musique
221 avenue Jean Jaurès 75019, Paris, France
+33 1 44848952
1 jpechard@cite-musique.fr
labo@cite-musique.fr
www.citedelamusique.fr/lab
Several diagnostic techniques are routinely applied at the research and conservation laboratory of the Musée de la musique in Paris to musical instruments belonging to its collections. In addition, more imaging methods are being developed to provide new insights into the conservation state of the instruments. In particular, we are implementing measurement techniques which are not primarily designed to produce images: spectrometries (UV-visible luminescence, X-ray Fluorescence, Fourier-Transform Infrared), acoustic measurements, etc., but where the data can be represented as maps (by simultaneous or sequential collections of spot analyses) or images (by the recent developments of 2D detectors).
laboratoire de recherche et de restauration du Musée de la musique - Cité de la musique
221 avenue Jean Jaurès 75019, Paris, France
+33 1 44848952
1 jpechard@cite-musique.fr
labo@cite-musique.fr
www.citedelamusique.fr/lab
Several diagnostic techniques are routinely applied at the research and conservation laboratory of the Musée de la musique in Paris to musical instruments belonging to its collections. In addition, more imaging methods are being developed to provide new insights into the conservation state of the instruments. In particular, we are implementing measurement techniques which are not primarily designed to produce images: spectrometries (UV-visible luminescence, X-ray Fluorescence, Fourier-Transform Infrared), acoustic measurements, etc., but where the data can be represented as maps (by simultaneous or sequential collections of spot analyses) or images (by the recent developments of 2D detectors).
This paper will present an overview of the use of these techniques in recent years at the Musée de la musique and discuss the foreseeable perspectives on current developments for conservation diagnostics.
More than 600 instruments have been examined using X-ray radiography since 1999, using the on-site equipment, to perform structural diagnostics (degradation and modification) and detect evidence of hidden signs of making techniques. The recording of every parameter for each radiography in a database allowed for their optimisation, and fast, reproducible shooting and image productions. Several studies included distortions effects, possibility of measurements on X-ray films, enlarged X-ray images, etc. A few experiments on medical X-ray tomographs for 3-dimensional imaging were impaired by the difficulties adapting instrumental parameters to the X-ray absorption of the musical instruments materials. Recent experiments on a violin using neutron and conventional X-ray sources (Paul Sherrer Institute facility, Villegen, Switzerland) have shown the great interest of neutron and X-ray computed tomography. The differences in sensitivity to heavy and light elements of both techniques, their respective advantages and disadvantages and their complementarity will be discussed.
The structure of a string instrument can then be used in mechanical modelling to assess and image the effect of future restringing or restoration work (for example) on the strain field, deformations, etc. This tool is particularly valuable in the case of instruments kept in playable conditions. The mechanical state of a soundboard instrument can also be investigated experimentally using acoustic holography, allowing among others things to gather evidence of structural modifications and defects which could occur with ageing.
Imaging techniques are also of interest at the micrometer scale, when applied to samples from musical instruments. Thus, wood micro-structure has been imaged on a micro-sample using X-ray micro-tomography (Spring-8 facility, Harima Science Park City, Japan), and using Optical Coherence Tomography, a non-contact and non-destructive technique, on an 18th century Italian violin. The prospects for the description of wood anatomy, identification of wood species, varnish penetration into wood, varnish layers structure, will be discussed, together with experimental constraints (type of materials which can be analyzed, samples dimensions, possible beam damages, etc.) and imaging outputs (spatial resolution, dynamic range, etc.).
Another important aspect is chemical imaging. Cultural heritage objects are often highly heterogeneous in terms of composition at the macro-, meso- and micro-scales and spot analyses are therefore often not representative, insufficient to describe the complexity of the piece/aspect studied. Elemental mapping using X-ray Fluorescence spectrometry is routinely available in the laboratory or in collections for in situ measurements of painted/varnished surfaces, metals or corrosion products identification, etc. Chemical mapping and imaging of varnish materials have also been recently performed at the (sub-) micrometer scale, on cross section micro-samples, using FTIR-spectromicroscopy, and UV-visible luminescence micro-imaging using synchrotron radiation (SOLEIL facility, Saint-Aubin, France). This allowed determination of the specific nature of each varnish stratum, including protein-based materials. Possible developments and perspectives of these non-invasive spectro-imaging techniques will be discussed.
Micro-destructive sampling techniques on historical musical instruments: analysis and new results R. Avagliano1, E. Basso1, C. Canevari2, M. Malagodi1
1 Laboratorio Arvedi – CISRiC, University of Pavia
via Ferrata 1, 27100 Pavia, Italy
+39 0382 985326
2 Civica Scuola di Liuteria di Milano
via Noto 4, 20124 Milano, Italy
+39 02 8844821
The evolution of new scientific techniques for chemical analysis improved the importance of micro-destructive practices of sampling, in some cases completely non-destructive, on historical musical instruments. The authors propose a new protocol based on taking micro-samples containing enough material for one stratigraphic sequence useful to different diagnostic analysis: examination in visible light microscopy, characterization of organic components by micro FT-IR spectroscopy and inorganic components by micro-Raman and examining the individual layers by electronic microscopy (SEM) and EDS analysis for the recognition of the main elements. A key role is played by the rules of sampling (the instruments and techniques used, quantity and depth of sampling, number of samples and areas of sampling, etc…) and pre-treatment (including cutting methods, surface treatment, possibility of using the same sample for multiple surveys). Once established operating conditions of sampling and refined the analytical approach, it will gain a wealth of information with a limited number of very small samples. The application of this methodology on a historical musical instrument (double bass L. Bajoni, Milan, 1868) will be discussed.
X-ray and neutron imaging as complementary non-destructive methods for investigations of historical brasswind instruments D. Mannes1, A. von Steiger2, E. Lehmann1, R. Egger3
1 Neutron Imaging and Activation Group, Spallation neutron source SINQ, Paul Scherrer Institute (PSI), Villigen, Switzerland
+41 56 310 4610
+41 56 310 3131
david.mannes@psi.ch
http://neutra.web.psi.ch
2 Bern University of the Arts, Bern University of Applied Sciences
3 Egger Blechblasinstrumentenbau, Münchenstein/Basel, Switzerland
+41 56 310 4610
+41 56 310 3131
david.mannes@psi.ch
http://neutra.web.psi.ch
2 Bern University of the Arts, Bern University of Applied Sciences
3 Egger Blechblasinstrumentenbau, Münchenstein/Basel, Switzerland
Historical instruments represent unique, irreplaceable and most often precious objects. Investigations of such instruments are a very delicate subject as the integrity of the examined instruments should not be altered. Such examinations can nevertheless be necessary as they represent the only way to gather information on:
- the actual condition of the instrument > essential information for conservators
- the construction of the instrument > answering the question how the sound is generated in comparison to instruments from other periods respectively to contemporary instruments
- the manufacturing procedure > historically relevant for the understanding of the manufacturing evolution; requirement for the reproduction of historically informed instruments
- the manufacturing procedure > historically relevant for the understanding of the manufacturing evolution; requirement for the reproduction of historically informed instruments
As consequence of the delicate nature of the objects non-destructive testing methods are predestined for investigations of historical instruments. In this work we present with X-ray and neutron imaging two complementary non-destructive testing methods based on transmission measurements of radiation. The experiments were carried out within the scope of a joint CTI-promoted project of the Bern University of the Arts, PSI, EMPA and Egger Blechblasinstrumentenbau the design and working processes of 19th century brass instruments are analysed in order to produce historically correct copies of the instruments. The project includes a broad variety of utilised methods, which are presented in the contribution “Looking over the Instrument Maker's shoulders“ by A. v. Steiger.
Neutron and X-ray imaging work along similar principles: an object is exposed to radiation (neutron or X-ray) and the intensity of the radiation behind the object is registered with a detector resulting in a shadow image. The emerging transmission images show different features depending on the elemental composition, the density and structure of the object and the radiation used. Neutron and X-ray images can differ considerably because both radiations are attenuated to a different degree by the different elements. The attenuation of X-ray is correlated with the atomic number of the elements; elements with higher atomic number, such as metals attenuate X-ray radiation more heavily, while light elements, such as organic matter is almost transparent. Neutron radiation on the other hand is transparent to some metals (aluminium, lead,…), while hydrogenous materials result in high attenuation. The two methods can thus be considered as complementary methods yielding more information, than one method alone could provide. The presented experiments were performed at the neutron radiography facility NEUTRA at the spallation neutron source SINQ at PSI with thermal neutrons and X-ray (Ex=150kV). The facilities are open to national and international users via scientific proposals. The services are normally free of charge for users from universities or research institutes (http://sinq.web.psi.ch/sinq/sinq_call.html).
Neutron and X-ray imaging work along similar principles: an object is exposed to radiation (neutron or X-ray) and the intensity of the radiation behind the object is registered with a detector resulting in a shadow image. The emerging transmission images show different features depending on the elemental composition, the density and structure of the object and the radiation used. Neutron and X-ray images can differ considerably because both radiations are attenuated to a different degree by the different elements. The attenuation of X-ray is correlated with the atomic number of the elements; elements with higher atomic number, such as metals attenuate X-ray radiation more heavily, while light elements, such as organic matter is almost transparent. Neutron radiation on the other hand is transparent to some metals (aluminium, lead,…), while hydrogenous materials result in high attenuation. The two methods can thus be considered as complementary methods yielding more information, than one method alone could provide. The presented experiments were performed at the neutron radiography facility NEUTRA at the spallation neutron source SINQ at PSI with thermal neutrons and X-ray (Ex=150kV). The facilities are open to national and international users via scientific proposals. The services are normally free of charge for users from universities or research institutes (http://sinq.web.psi.ch/sinq/sinq_call.html).
In the presented experiments neutron respectively X-ray sensitive imaging plates were used for detection. These provide satisfactory spatial resolution (50µm/pixel) and a large field of view at the same time. Nevertheless three to five images from different sections had to be taken to cover the whole instrument. The sections images were subsequently reassembled yielding images of the complete instruments. The spatial resolution can be increased to ca. 13.5 µm/pixel using a different detector system.
The transmission images show a couple of features such as the overall density distribution, plug connections, join patches, which are visible with both types of radiation. Other features are only visible in one or the other image. The neutron images allow for a measurement of the wall thickness; prominent are all hydrogenous substances (e.g. leather pads in keys, condensation water from playing). The X-ray images yield further information on material irregularities or the distribution of soldering material.
Both methods work non-destructively and can yield precious information on the inner structure, the built-up and composition of historical instruments. Neutron imaging and X-ray imaging can be regarded as complementary, hence the highest gain in knowledge can be achieved, when using a combination of both methods.
Dating musical instruments: a proposal for investigation, G. Maino1, 2
Dating musical instruments: a proposal for investigation, G. Maino1, 2
1 ENEA
via Martiri di Monte Sole 4, 40129 Bologna, Italy
+39 0544 6098206
+39 0544 6098206
2 University of Bologna, Ravenna site
Via Mariani 5 (Palazzo Corradini), 48121 Ravenna, Italy
+39 051 6098206
I present and discuss the main scientific techniques for dating artistic and historical objects, with reference to applications to musical instruments. Limits of applicability, feasibility and precision of different methods are critically assessed. A proposal for future investigation is finally addressed.
Virtual solution for enhancing knowledge and fruition of musical instruments, M. Panebarco1, C. Panebarco1
1 Panebarco & c. - virtual solutions
via Molino 9, 48121 Ravenna, Italy
+39 0544 35012
In recent years virtual solutions have been used in several fields to enhance comprehension of complex machinery, to train qualified employers, to visualize chimical reactions... cultural heritage is only partly exploiting the opportunities offered by 3d reconstructions and virtual reality. Virtual solutions could represent an amazing opportunity for the fruition, promotion and also preservation of cultural heritage. The current presentation will take into account two solutions in particular (Exhibits3d, a real time 3d engine for single player virtual visits, and VirtualLife, a virtual world platform) and will suggest specific applications for the fruition of musical instruments.
Microsoft Access© based conservation form used in the civic museum of musical instruments in Milan, E. Marconi, external conservator1, F. Tasso, chief curator1
1 Civic Museum of Musical Instruments
Castello Sforzesco, piazza Castello, Milan, Italy
+39 02 88463730
In 2005 at the Civic Museum of musical Instruments in Milan has been projected and developed a Microsoft Access© based conservation form: the goal was to provide the curator a light and simple tool (as much as possible user friendly) able to collect all the information existing in the museum’s archives about each musical instruments of the collection (catalogue, images, scientific studies carried out, …) and, on the other hand, to allow the conservator to have a computerized conservation form to fill on periodical basis. At the moment, more than 200 has been filled.
The software’s choice was made, following a list of criteria:
- must not be expensive: freeware or already bought and installed on museum’s pc
- must be user friendly
- must be sharable as much as possible with other Italian museums or into the public administration
Microsoft Access© satisfied 2 conditions:
- already installed in the Museum’s pc
- largely used in the Italian public administration
The upper part of the form allows to identify the object (inventory number, image and some historical data) and then to identify the position into the museum or the storage, through a text field and a map.
Just below, some fields are dedicated to the exhibitions system (with relation to the materials in touch with the object), and to the overall, structural and surface conditions (linked to the possibility - or less - to move safely the object).
One of the first goal is to understand immediately the eventual fragilities of the object, in order to be very conscious of then, when moving, cleaning, or studying the musical instruments.
Every kind of file can be linked to the form (image, text, pdf, audio, video).
When the form has been filled, all the information about the object has been digitized and can be consulted through the database.
The use of Wikimedia software in the web data sharing process between makers, restorers and conservators of musical instruments R. Regazzi, luthier and restorer
via Angelo Musco 1, 40127 Bologna, Italy
The free opensource server-side software created by the Wikimedia Foundation became in the last ten years a powerful tool also for those who are working with musical instruments.
In a recent private experiment some relevant modifications of the original package were introduced in order to adapt it to a more specialized use in this area.
The experiment, which reached up to now about 90000 stored pages, showed some promising eesults, so that the idea to structure it to a larger-scale possible usage came into mind.
Such a dedicated complex platform is simplyfied by an innovative use of special templates, which are bringing the possibility of easy data input and sifting of many kinds and an effective way of sharing specialized information between several levels of users.
The system benefits from a great number of extensions continuously developed all over the world, so that new controls and features may be applied at any time to the same base of data, at a very little or even zero maintenance cost.
This paper explains how the adapted software can be useful for a number of cataloguing projects and opens up a discussion if it might be suitable and advisable for a wide shared use in our field.
In particular three recently started sub-projects -such as "portals" in a true sense - are presented in a practicle
way:
A) the Permanent Universal Dictionary of makers, restorers and dealers,
B) the Permanent Register of relating musical instruments (with data and pictures)
C) the Permanent Literature Collection (pertaining bibliography)
Synchrotron radiation microtomography of bowed stringed instruments: the 1753 violin by G.B. Guadagnini N. Sodini1
1 Sincrotrone Trieste
Strada Statale 14 - km 163,5
34149 Basovizza - Trieste, Italy
+39 040 3758558
nicola.sodini@elettra.trieste.it
Strada Statale 14 - km 163,5
34149 Basovizza - Trieste, Italy
+39 040 3758558
nicola.sodini@elettra.trieste.it
X-ray computed tomography (CT) is becoming a common technique for the structural analysis of ancient manufacts of cultural relevance, providing luthiers, art historians, conservators and restorators with a unique tool for the characterization of musical instruments. CT-derived information aid in the replication of original masterpieces and have an important role in the valuation, insurance, and identification of valuable stringed instruments.
The value of an historical instrument may decrease considerably if a defect or repair is discovered. For example, a violin with a crack in the sound post region of the back plate is conventionally valued at only 50% of the same instrument without the defect. Moreover, it is well known that many serious abnormal conditions may be concealed with glue, filler material, retouch, or varnish. Abnormal conditions that affect bowed stringed instruments include cracking, warping, and wormholes (caused by the infestation of larvae).
Unfortunately, conventional tomographic systems are unable to reach the desired spatial resolution (i.e. between 10 and 50 microns) or are able to analyse a whole instruments due to the reduced field of view of X-ray detectors and/or the dimensions of the commercial X-ray hutches. After the first feasibility studies, carried out at the SYRMEP beamline of the Elettra synchrotron laboratory in Trieste, showing the advantages and evaluating the effectiveness of synchrotron radiation X-ray microtomography, the first analysis of a instrument of historical importance (the 1735 violin by Giovan Battista Guadagnini) has shown the full potential of the technique. Together with a full and detailed description of the different modifications applied to the violin during the years, we were able to test and confirm the reliablity of the environmental setup (for temperature and humidity control during the data acquisition). Some consideration related with the dendrochronological investigation of historical violins will be described.
Looking over the Instrument Maker's shoulders. Methods of material analysis of production technology for brasswind instruments A. von Steiger1
1 Bern University of the Arts
Fliederweg 10, CH-3098 Köniz, Switzerland
+41 31 972 46 62
+41 79 642 34 48
www.hkb.bfh.chResearch on the history of instrument making can follow two courses: the historical and the analytical.
A combination of the two, depending on the sources available, produces astonishing rich results.
The research considered in this paper has been carried out most recently in 2010 at the University of the Arts in Bern in a multidisciplinary collaboration with material-scientists, instrument makers and
musicians. It explores brasswind instrument production in nineteenth-century France. The source material is variable: a great number of instruments have been preserved, but written sources regarding their construction are rare. Intact workshops, contemporary pictures and bankruptcy inventories have proven to be the most reliable sources. From these we know what work was done. However, these sources do not answer the question of how it was done.
Methods of material analysis may be able to answer this question; they allow us to observe the instrument maker at work. The methods used in our research are tomography, wall-thickness measurements, x-ray fluorescence and metallography. Together they create a complex analysis tool that in combination provide comprehensive evidence. The first three methods are non-invasive and were carried out on a large number of instruments. Metallography, however, is invasive. It can be used for a few probes and produces conclusive results regarding historical material handling processes such as soldering, hardening and annealing techniques, which cannot be determined from the other procedures.
Piano’s forgery revealed by dendrochronology D. Houbrechts1, P. Vandervellen2
1 Liege University, Laboratory of Dendrochronology
2 Musée des instruments de musique (MIM), Director
rue Montagne de la Cour 2, B-1000 Bruxelles, Belgium
+32 2 545 01 48
In the beginning of the year 2000, the Musical Instruments Museum (MIM), Brussels, bought in a public auction at Drouot, Paris, a piano which was reputed to be the oldest Belgian one in existence. On basis of an inscription behind the nameboard, the instrument was presented in the sales catalogue as the “first piano-forte made in 1771 in the city of Brussels”. But, when the instrument arrived at the museum, many collections’ curators had doubts concerning the authenticity of the instrument. Fortunately, there exists a law in France, which protects the buyer in a public sale. If you can prove that the item you have bought is a fake, you can obtain your money back. However, the onus is on the purchaser to prove that the object is a forgery.
One way to ascertain if an instrument is genuine is to determine if the age of the wood corresponds to the date of manufacture. So, the MIM asked David Houbrechts and his team of the Liege University, Laboratory of Dendrochronology to carry out a dendrochronological study of the instrument. The analyses show that:
- the soundboard is made up of 6 boards with different growth rates, thus boards coming from different trees - a fact a priori strange or paradoxical in instruments making where builders in principle look for the highest degree of homogeneity of material when constructing soundboards,
- the most recent annual growth ring of the wood to… 1905.
Shortly after this misadventure, Pascale Vandervellen began a doctorial thesis on the manufacture of Belgian pianos. She has identified more than one hundred Belgium made instruments in public and private collections. Some bore a manufacture date but the majority did not. To help to date them, and/or verify their authenticity – like in the case of the instrument bought at Drouot – the MIM called for a second time upon for the Laboratory of Dendrochronolgy, Liege. Pascale Vandervellen also wanted to have answers to some questions linked to the soundboard. It is generally agreed that the soundboard of a piano, as with a violin, is one of the most important parts of the instrument. The type and cut of the wood used to construct it; how it is fixed in the instrument; its auxiliary supports; all have a determining effect on the sound produced. But no previous study has systematically examined the choices of wood made by the different manufactures.
So, in 2002, the Musical Instruments Museum and the Laboratory of dendrochronology made an agreement to study twenty-one instruments. We started with nineteen square pianos, these being the oldest Belgian pianos in the museum collection. We also decide to analyse three foreign square pianos in order to be able of compare the results with those obtained from the Belgian ones. Two years later, given the excellence of results obtained, the agreement between both institutions was extended to include twelve more pianos to complete the corpus. Five more square pianos, six grand pianos, and one cabinet-piano were chosen. All these pianos were made in Belgium, and preserved in public and private collections in Belgium, France, and Austria.
Altogether, thirty-five pianos were studied. To our knowledge, it was the first time that such a large coherent group of pianos was subjected to a dendrochronological study.
MIMO – Musical Instrument Museums Online L. Bognetti1,2, A. Myers3
1 University of Firenze, Italy
2 Galleria dell'Accademia, Dip. Strumenti Musicali, Firenze, Italy
3 Edinburgh University Collection of Historic Musical Instruments
Reid Concert Hall, Bristo Square,
Edinburgh EH8 9AG, U.K.
The MIMO project is a project of the European Community coordinated by the University of Edinburg with the ai of creating a single access point to digital content and information on the collections of musical instruments held in European museums.
At present, there is no common access point for anyone wishing to explore these collections online, nor is there any consistency or common standard for the online presentation of musical instruments. Taken as a whole, this important heritage is currently only accessible (with some difficulty) to scholars and museum professionals through the individual museums’ websites: this project seeks to address that problem. The MIMO project, which is funded through the European Commission’s eContentplus programme, will enable the digital content of eleven major musical instrument museums from across Europe to be harvested from their collection databases and made available to all through EUROPEANA, the European Digital Library.
While most of the partners have a significant proportion of their collections digitised in some capacity, few have much of this material available online. Through the targeted digitisation of well-defined groups of instruments, MIMO will create a common, easily accessible online information point. The project will digitise 35,000 musical instruments currently held in public collections. By adding these to 10,000 existing digital images, this will create a critical mass of 45,000 images of instruments, with metadata, thus making available 40% of Europe’s and 16% of the world’s heritage of historic musical instruments in public possession.
1,250 digital audio files giving an impression of the instruments’ sound will also be made available; 550 others will be digitised from analogue sources.
Even rarer, and thus more precious, are video clips of historic musical instruments being played. The project will provide 300 video clips, of which 200 will be digitised.
Another key aim of this project will be to improve multilingual access to content. This will be achieved through the delivery of dictionaries for controlled vocabularies for musical instruments databases. This will ensure consistency of classification for the musical instruments within a multilingual framework comprising the following languages: French, German, Italian, Dutch, Swedish and English.
The partners of the MIMO project are:
- University of Edinburgh, UK
- Germanisches Nationalmuseum, Nürnberg, Germany
- University of Leipzig, Museum für Musikinstrumente, Germany
- Africamuseum, Tervuren, Belgium
- Galleria dell’Accademia, Dip. Strumenti Musicali,” Firenze, Italy
- Cité de la Musique, Paris, France
- Musical Instrument Museum, Brussels, Belgium
- Università degli Studi di Firenze, Italy
- Horniman Museum, London UK
- Stiftung Preußischer Kulturbesitz Ethnologisches Museum, Berlin, Germany
- The Stockholm Music Museum, Sweden
The emulation of nonlinear musical instruments by means of volterra series, L. Tronchin
DIENCA - CIARM - University of Bologna, Italy
viale Risorgimento, 2
I-40136 Bologna, Italy
+39 051 2090542
The measurement and emulation of musical instruments and audio systems have been analyzed in these years. The most-used methods to obtain information about an audio system are those based on measuring its impulse response (IR). Once the IR has been caught it is possible to recreate, by the use of linear convolution, the output signal that the audio system will generate when it is physically driven by any input signal. This method gives great results if the system is linear and time-invariant (environments behaviour is much linear and therefore its reverberant effect can be faithfully recreated using IRs) but not satisfactory in other cases, such as the emulation of tube preamps (mainly nonlinear) and musical instruments. Since the musical instruments cannot be considered completely linear, their musical performance might be analysed properly considering also their nonlinear behaviour.
By using Volterra series it is possible to represent the input-output relationship of nonlinear systems. This mathematical theory uses a set of impulse responses to describe the system and not only one as before. By an enhanced impulse response measurement method it is possible to obtain this set of impulses and then with Volterra series it would be possible to have the output of the audio system driven by any input. A special numerical tool has been developed to recreate the system behaviour by using this method. Satisfactory results have been obtained in comparison with the traditional linear convolution based approach.
By using Volterra series it is possible to represent the input-output relationship of nonlinear systems. This mathematical theory uses a set of impulse responses to describe the system and not only one as before. By an enhanced impulse response measurement method it is possible to obtain this set of impulses and then with Volterra series it would be possible to have the output of the audio system driven by any input. A special numerical tool has been developed to recreate the system behaviour by using this method. Satisfactory results have been obtained in comparison with the traditional linear convolution based approach.
