# 10. Driving functions for LSFS¶

The reproduction accuracy of WFS is limited due to practical aspects. For the audible frequency range the desired sound field can not be synthesized aliasing-free over an extended listening area, which is surrounded by a discrete ensemble of individually driven loudspeakers. However, it is suitable for certain applications to increase reproduction accuracy inside a smaller (local) listening region while stronger artifacts outside are permitted. This approach is termed LSFS in general.

The implemented Local Wave Field Synthesis method utilizes focused sources as a distribution of virtual loudspeakers which are placed more densely around the local listening area. These virtual loudspeakers can be driven by conventional SFS techniques, like e.g. WFS or NFC-HOA. The results are similar to band-limited NFC-HOA, with the difference that the form and position of the enhanced area can freely be chosen within the listening area.

The set of focused sources is treated as a virtual loudspeaker distribution and their positions \({\x_\text{fs}}\) are subsumed under \(\mathcal{X}_{\mathrm{fs}}\). Therefore, each focused source is driven individually by \(D_\text{l}({\x_\text{fs}}, \w)\), which in principle can be any driving function for real loudspeakers mentioned in previous sections. At the moment however, only WFS and NFC-HOA driving functions are supported. The resulting driving function for a loudspeaker located at \(\x_0\) reads

which is superposition of the driving function \(D_{\mathrm{fs}}(\x_0,{\x_\text{fs}},\w)\) reproducing a single focused source at \({\x_\text{fs}}\) weighted by \(D_\text{l}({\x_\text{fs}}, \w)\). Former is derived by replacing \(\xs\) with \({\x_\text{fs}}\) in the WFS driving functions and for focused sources. This yields

and

for the 2.5D case. For the temporal domain, inverse Fourier transform yields the driving signals

while \(d_{\mathrm{fs}}(\x_0,{\x_\text{fs}}, t)\) is derived analogously to from or . At the moment \(d_{\mathrm l}({\x_\text{fs}}, t)\) does only support driving functions from WFS.