Add function to calculate the array manifold of an arbitrary array

Signal Processing/Array Processing/MATLAB/Functions/arrMan.m

+%% Calculate the array manifold (steering vector) of an arbitrary array
+% --------------------------------------------------
+% Author: Achilles Kappis
+% e-mail: axilleaz@protonmail.com
+%
+% Date: 28/05/2024 (DD/MM/YYYY)
+%
+% Copyright: MIT
+% --------------------------------------------------
+% Functionality: Calculate the array manifold (steering vector) of an
+%                arbitrary array.
+% --------------------------------------------------
+% Input
+% 
+% mPos [numeric]: The positions of the sensors in Cartesian coordinates.
+%                 This must be an Mx3 matrix where M denotes the number of
+%                 sensors and for each sensor the coordinates are in
+%                 [x, y, z] format.
+% 
+% dirs [numeric]: These are the directions for which the array manifold
+%                 will be calculated. This must be an Nx2 matrix where N is
+%                 the number of directions and for each direction the
+%                 azimuth and elevation/inclination is given. The values
+%                 must be provided in radians. The directions must be
+%                 pointing towards the incoming plane waves and not towards
+%                 the array/origin.
+% 
+% k [numeric]: The wavenumbers of interest. This must be a vector
+%              containing all the wavenumbers for which the array manifold
+%              will be calculated.
+% 
+% --------------------------------------------------
+% Output
+% 
+% am [numeric]: The array manifold/steering vector of the array for the
+%               directions/angles and wavenumbers provided. The dimensions
+%               of the argument are MxNxK where M is the number of sensors,
+%               N the number of directions/angles and K the number of
+%               frequencies/wavenumbers.
+% 
+% --------------------------------------------------
+% Notes
+% 
+% --------------------------------------------------
+function am = arrMan(mPos, dirs, k)
+    % ====================================================
+    % Check for number of arguments
+    % ====================================================
+    narginchk(3, 3);
+    nargoutchk(0, 1);
+
+    % ====================================================
+    % Validate input arguments
+    % ====================================================
+    % Validate mandatory arguments
+    validateattributes(mPos, "numeric", {'2d', 'finite', 'nonnan', 'nonempty', 'real', 'ncols', 3}, mfilename, "Position of sensors", 1);
+    validateattributes(dirs, "numeric", {'2d', 'finite', 'nonnan', 'nonempty', 'real', 'ncols', 2}, mfilename, "Directions of interest", 2);
+    validateattributes(k, "numeric", {'vector', 'finite', 'nonnan', 'nonempty', 'nonnegative', 'real'}, mfilename, "Wavenumbers of interest", 3);
+
+    % =============================================
+    % Calculate the array manifold
+    % =============================================
+    % Get Cartesian coordinates of directions
+    [x, y, z] = sph2cart(dirs(:, 1), dirs(:, 2), ones(size(dirs(:, 1))));
+
+    % Inner product of directions and sensor position
+    am = mPos * [x, y, z].';
+
+    % Multiply with wavenumbers
+    am = am .* permute(k(:), [3, 2, 1]);
+end
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