Vía de activación del receptor del factor de crecimiento epidérmico

All of the above uses of WFS are subject to the inherent errors of WFS such as discretisation, spatial aliasing and truncation effects/edge effects. Truncation errors are caused by the finite length of the arrays used for the reproduction, causing diffraction errors at the end of the arrays. Edge errors are also caused in the corners where two loudspeaker arrays meet. Whilst these can be minimised by adopting various filtering schemes, there are consequent limits on the available applications of WFS. Analyses of the errors inherent in WFS reproduction due to the size of the arrays being used to reproduce the signals and the discretisation of the array can be found in (Spors and Rabenstien, 2006; Start, 1997; Verheijen, 1998)

Much research is still to be done in the area of WFS, looking at the optimisation of the WFS reproduction and coding, subjective effects resulting from simplifications that are made, evaluation and prediction of wave fields, novel applications of WFS, perceptual effects and dual modality investigation when using WFS with 2- dimensional or 3-dimensional displays. Consequently there is an ever increasing body of research into this exciting subject of wave field synthesis. This thesis aims at

the characterisation and improvement of focused sources in WFS, which is an under- researched area so far despite the many novel applications and interesting properties of such sources.

3.8 Summary

This chapter has presented the background theory of the wave field synthesis sound field reconstruction technique. A comprehensive theoretical background has been presented, including the foundational mathematic constructs and a detailed derivation of the important driving functions used throughout this thesis. A brief analysis of some of the reproduction artefacts of WFS has also been described in this chapter including, amplitude errors, spatial sampling artefacts and truncation errors. Many of these errors are common to both focused and non-focused sources although the manifestation of the artefacts will be different for focused sources. This chapter has described only non-focused sources, the next chapter deals specifically with the objective analysis of WFS focused sources and the errors there inherent.

Having laid the theoretical background of WFS, the chapter then described the design, installation and calibration of four WFS systems that have been installed at the University of Salford that have been used in the work described in this thesis. Also covered is a generic literature review, presenting an overview of the main areas of research in WFS since its conception in the late 1980’s.

4

Objective Analysis of WFS Focused

Sources

4.1 Introduction

The ability of sound reproduction techniques based on physical principles and a sound field description such as wave field synthesis to recreate acoustic wave fronts of an arbitrary shape allows for the reproduction of so-called focused sources. Focused sources are in fact not really sources but rather they describe the focusing of acoustic energy to a point in space. As the point does not behave like an acoustic sink, the acoustic energy peaks at the ‘focal point’ and then re-radiates from there, giving the impression of a source at that point. This is a remarkable attribute of WFS systems and allows for several interesting applications. For example, focused sources can be used for 3D virtual reality systems such that the depth of the acoustic source matches more perfectly the depth of the visual source being generated/projected (Boone et al., 1996). Focused sources have also been showed to be useful for creating virtual loudspeaker signals in hybrid systems (Menzel et al., 2005).

In the strictest sense, focused sources in WFS cannot be fully described by the Kirchhoff-Helmholtz equation demonstrated in the previous chapter. The Kirchhoff- Helmholtz equation states that the volume in question should be source free whereas a focused source expressly describes a volume with a source present. However this is not a real source but rather the appearance of a source thus the method of derivation used for normal WFS sources also stands in this case.

This chapter begins with a brief overview of sound focusing techniques and describes some of the properties of the produced focused wave fields. The chapter then goes on to describe the driving functions for the main focused source models used for practical WFS implementations including monopoles, dipoles and pistonic sources. Following this is a description of the secondary source selection criteria specific to the reproduction of focused sources and the necessary correction needed for symmetrical rendering and directed sources. The primary attributes of focused sources in WFS are then described including amplitude errors, truncation and spatial aliasing errors, causality and pre-echo artefacts, focal spot size and phase response. A model is also derived to predict the position error in focused source as a result of the focal shift phenomena caused by diffraction effects at low frequencies. A full description of spatial aliasing artefacts, including an analytical expression for the position dependant spatial aliasing condition for focused sources and the definition of the aliasing-free zone in the near vicinity of the focal point is also presented. The chapter concludes with some discussions on the rendering of moving sources and sources using large arrays.