hello
- basically you want to plot the envelope of your data , there is a function for that :
envelope Envelope detector.
[YUPPER,YLOWER] = envelope(X) returns the upper and lower envelopes of
the input sequence, X, using the magnitude of its analytic signal.
it requires the Signal Processing Toolbox
- you may want to remove first the spikes , so a bit of low pass filtering / smoothing is needed
you can do that with smoothdata
If you don't have the Signal Processing Toolbox, see the demo below :
t = 0:0.01:10;
x = exp(-(t-5).^2/2).*sin(2*pi*5*t);
% obtain the envelope data
%--------------------------------------------
y = abs(hilbert(x)); % option 1 with hilbert
[up,down] = envelope2(t,x,'linear'); % option 2 with envelope2 (see below)
plot(t,x,t,y,'k',t,up,'m',t,down,'c')
legend('signal','hilbert','envelope2 / upper env','envelope2 / lower env');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [up,down] = envelope2(x,y,interpMethod)
%ENVELOPE gets the data of upper and down envelope of the known input (x,y).
%
% Input parameters:
% x the abscissa of the given data
% y the ordinate of the given data
% interpMethod the interpolation method
%
% Output parameters:
% up the upper envelope, which has the same length as x.
% down the down envelope, which has the same length as x.
%
% See also DIFF INTERP1
% Designed by: Lei Wang, <WangLeiBox@hotmail.com>, 11-Mar-2003.
% Last Revision: 21-Mar-2003.
% Dept. Mechanical & Aerospace Engineering, NC State University.
% $Revision: 1.1 $ $Date: 3/21/2003 10:33 AM $
if length(x) ~= length(y)
error('Two input data should have the same length.');
end
if (nargin < 2)|(nargin > 3),
error('Please see help for INPUT DATA.');
elseif (nargin == 2)
interpMethod = 'linear';
end
% Find the extreme maxim values
% and the corresponding indexes
%----------------------------------------------------
extrMaxIndex = find(diff(sign(diff(y)))==-2)+1;
extrMaxValue = y(extrMaxIndex);
% Find the extreme minim values
% and the corresponding indexes
%----------------------------------------------------
extrMinIndex = find(diff(sign(diff(y)))==+2)+1;
extrMinValue = y(extrMinIndex);
up = extrMaxValue;
up_x = x(extrMaxIndex);
down = extrMinValue;
down_x = x(extrMinIndex);
% Interpolation of the upper/down envelope data
%----------------------------------------------------
up = interp1(up_x,up,x,interpMethod);
down = interp1(down_x,down,x,interpMethod);
end
