MATLAB: Grabbing number from array to calculate the numerical derivative

Question

Hello,

I ma looking for solution that will allow me to calculate a derative (in numerical way) from data from array.

I have an array caled DataOutput it's defined as:

DataOutput = zeros(length(phiAStart:phiAStep:phiAEnd),30);

where :

phiAStart:phiAStep:phiAEnd

are defined by a user (as input)

In this array, I have two columns that I would like to further work with. In column 1 I have "x" and in column 26 I have a "y"… where y=f(x) and x value is incremented by loop function:

for x=phiAStart:phiAStep:phiAEnd 
    ...
end

Now what I would like to do is calculate a derivative and store it in another array (or even in the same if its possible). For calculation I would like to use simple formula:

f'(n)=((y(n+1))-(y(n-1)))/((x(n+1))-(x(n-1)))

For clarification this is how it's done in excel sheet:

I am assuming that I will need another for loop outside of the previous one but I am not sure how I should define a formula for this sort of equation (especially how to define new vectors).

I would be thankful for any idea.

Answer 1

For the version you post, see the diff( ) function along with element-wise divide. E.g.,

diff(y) ./ diff(x)

If that doesn't work well enough for you, you could explore central difference formula versions, or perhaps some type of curve fit.