Matlab function for computing the rms integrating from high frequency to low frequency. Has additional option to clip the integration to some frequency upper bound.

rms2.m

function [x_clipped, rms] = rms2(x, y, varargin)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%						
%	find the rms value of y(x)		
%	y(f) could be a spectral density	
%	or y(t) could be a time series		
%	
%   optional var sets the cutoff of x to compute
%   from.  This will shorten the output vector
%   and returns x_clipped, yRMS intergrating from
%   top to bottom
%
%	usage: rmsY = rms(X,Y);		
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Assert and handle input because matlab is terrible
if isempty(varargin)
    f_upperB = max(x);
elseif length(varargin) == 1
    f_upperB = varargin{1};
else
    error("Too many optional argments passed in")
end

% Assert x and y are vectors with some length longer one form nx1 or 1xm
if ~xor((size(x,1)==1),(size(x,2)==1))
    error("Input data x must be vector")
end
if ~xor((size(y,1)==1),(size(y,2)==1))
    error("Input data y must be vector")
end

% Handle translation of input vectors to form 1xm
if size(x, 2) == 1
    x = x';
    trasposeOutput_x = true;  % Remember to tranpose on output
else
    trasposeOutput_x = false;
end
if size(y, 2) == 1
    y = y';
    trasposeOutput_y = true;  % Remember to tranpose on output
else
    trasposeOutput_y = false;
end

% Apply clipping of x range, if given by input, else default to full range
if (max(x)>f_upperB)
    x_clipped = x(1:find(x > f_upperB, 1));
    y_clipped = y(1:find(x > f_upperB, 1));
else
    x_clipped = x;
    y_clipped = y;
end

dx = diff(squeeze(x_clipped));
dx = [x_clipped(1) dx];

rms = fliplr(sqrt(cumsum(fliplr((squeeze(y_clipped).^2.*dx)))));

% Transpose outputs to match input
if trasposeOutput_x
    x_clipped = x_clipped';
end
if trasposeOutput_y
    rms = rms';
end

end