How much a signal curves

I asked a question earlier in : math.stackexchange, It was the follwing :

I have a random signal, and i need a way in simulink to find how much this signal curves (the result will be a signal also proportional to how much the first one will curves, it doesn't matter if it's going up or down, all i care about if how much it curves).

In the answer the guy said i should use a double derivative or an integrator ? i tried, but it doesn't seem to work.

[Image Analyst]

Show screenshots of your data. Why not simply compute the difference between a starting value and ending value? The bigger the difference, the more the signal must have curved, right? What's your definition of curves? Maybe the definition to be used will depend on what you plan on doing with the information. What will you do with the curvature number if you can get it?

[John BG]

do you mean you want the Simulink amplifier? or the Simulink block d/dt ?

[John D'Errico]

Is the signal noisy? If so, then you probably want to use a Savitsky-Golay filter to estimate the local second derivative of your series. Take the absolute value of that second derivative. Where it is large, your function is curved.

In MATLAB, conv can do the work. I have no idea how to make it work in simulink.

If you need to know how to calculate the coefficients of the corresponding kernel, that part is easy enough.

Answer 1

[John D'Errico]

In MATLAB, I would do this:

n = (-5:5)';
A = [n.^2,n,ones(size(n))];
P = pinv(A);
SGfilt = P(1,:)/2
SGfilt =
  0.0087413    0.0034965  -0.00058275   -0.0034965   -0.0052448   -0.0058275   -0.0052448   -0.0034965  -0.00058275    0.0034965    0.0087413

d2 = conv(Y,SGfilt,'valid');
plot(d2)

Where the result is large, the function is curved.

Note that noise will tend to be amplified, so on noisy data, you need to use a longer convolution kernel. Thus, n must have a larger span when the noise will be large.