I have a set of signals (Fourier series produced varying the sine and cosine parameters) and I would like to find the upper and lower envelope of this set.
A workable example of the Fourier series is:
%interval length and number of points
L = 2*pi;
N = 60;
%data points
x = (linspace(0,L,N+1))';
s1 = 1*sin(x) + 2*cos(x) + 3*sin(2*x) + 4*cos(2*x);
s2 = 4*sin(x) + 1*cos(x) + 2*sin(2*x) + 3*cos(2*x);
s3 = 3*sin(x) + 4*cos(x) + 1*sin(2*x) + 2*cos(2*x);
#
clf;
plot(x, s1, 'k', x, s2, 'b', x, s3, 'r' )
#
How can I compute the envelopes I need?
Thanks to @Tasos Papastylianou, I found a solution. It is enough to arrange the signal values in a matrix and take the minimum and maximum values for each row:
#To find envelope: arrange the function values in matrix
#And take max and min by row
foo = [s1, s2, s3];
env_hi = max(foo,[], 2);
env_low = min(foo, [], 2);
#
clf;
hold on;
plot(x, s1, 'g', x, s2, 'b', x, s3, 'r' )
plot(x, env_low, 'k^', x, env_hi, 'kv')
legend('s1', 's2', 's3', 'env-low', 'env-hi', 'location', 'north');
#