WFS 2.5D focused source time driving function does not match theory

[chris-hld]

For 2.5-D WFS, getting the time based driving signals for a focused virtual source:

• g0 of the default implementation does not match the referenced equation in the docu.

I tried both, and there is a difference in resulting amplitude. Which one should be preferred?

[hagenw]

Interesting. This should be fixed in #124

[fietew]

Imho, the documentation is wrong.

[hagenw]

The documentation is in line with Schultz (2016), or do we have the same problem there that the values are defined differently? I'm also not sure if the equations in Verheijen (1997) and Start (1997) are different due to other definitions of the distances or if they are really different ;)

[fietew]

Does Schultz (2016) cover focused sources at all?

[hagenw]

It doesn't, but as it should be only the time reversed version and |x0-xs| and |xref-x0| should be ok, as the sign does not matter.

[fietew]

If you do the math, especially the stationary phase approximation, there is a difference which stems from the time reversal. For the exponential term inside the synthesis integral you get exp(-j k (|x0 - xs| + |x0 - x|)) for a point source and exp(-j k (- |x0 - xs| + |x0 - x|)) for a focussed source. The second distance term |x0-x| is the green's function on the boundary and does not change with time reversal. The argument of the exponential directly corresponds to the denominator of g0.

[hagenw]

OK, I have now tested it with test_wfs_25d() and looked at the fact that the source in inside the listening area. Now, I would also say that the implementation is correct and the documentation is wrong. I will create a pull request for the documentation.

[fs446]

Nope

On 21 Dec 2016, at 8:10 PM, Fiete Winter notifications@github.com wrote:

Does Schultz (2016) cover focused sources at all?

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[hagenw]

This is now fixed.