http://www.k-wave.org/forum/topic/maximum-frequency-on-a-given-grid-in-several-dimensions Support for the k-Wave MATLAB toolbox en-US Tue, 12 May 2026 23:28:21 +0000 http://bbpress.org/?v=1.0.2 q http://www.k-wave.org/forum/search.php http://www.k-wave.org/forum/topic/maximum-frequency-on-a-given-grid-in-several-dimensions#post-5390 Tue, 16 Feb 2016 02:39:57 +0000 Bradley Treeby 5390@http://www.k-wave.org/forum/ <p>Hi Anthony,</p> <p>Interesting question! If you consider the grid geometrically, it would seem that the points are spaced further apart in the diagonal direction, and therefore would support a lower maximum frequency.</p> <p>However, if you think about the wave propagation in k-space, the wave field is broken into a sum of plane waves propagating in different directions. These directions are given by the values of kx and ky. Because the discrete k-space grid is square, the grid actually supports slightly higher maximum frequencies in the diagonal directions, as the corners of the k-space have a higher wavenumber than the limits of the vertical and horizontal axes.</p> <p>Hope that helps,</p> <p>Brad, </p> http://www.k-wave.org/forum/topic/maximum-frequency-on-a-given-grid-in-several-dimensions#post-5331 Fri, 27 Nov 2015 11:09:35 +0000 Anthony 5331@http://www.k-wave.org/forum/ <p>Hello everyone,</p> <p>I have a question about the maximum frequency which can be propagated in several dimensions. In 1D, Shannon-Nyquist says that you need at least two points per wavelength.</p> <p>But, in 2D, if you wave does not propagate in the direction of your basis vectors, don't you need up to 2*sqrt(2) points per wavelength ? (and 2*sqrt(3) in 3D...) ? Am I right? </p> <p>Best regards,<br /> Anthony</p> <p>EDIT: Sorry, I just made the calculations on a rectangular grid with Peterson-Middleton theorem and it seems enough to have two points per wavelength :-) It seems counter-intuitive to me though... Anyway, sorry, I shouldn't have posted ;-) </p>