How can one calculate Differentiation of matrix array with time as first column and data as second column ?

Hello everyone,

I have a problem solving the differentiation of vector. I have data with first column as time and second column as my data. Now, I want to calculate the derivative of this data and again want the matrix with same size. So, does anyone have any idea how can I make it ??

My matrix has 80,000 data value with time. So, I have 80,000 rows and 2 columns which are time and data values.

Please help me with this.

In another way i can explain as, suppose I have a data of ramp input and there are 80,000 point values for specific time values. So, now I want to calculate derivative of this ramp input. So, If you have any idea please help me.

If you still have doubt then please write in comment. I will try to explain it more in details.

Thank you.

Answer 1

[dpb]

g=diff(v(:,2))./diff(v(:,1));       % numerical gradient

The gradient vector estimate will be one element shorter than the input vector; if for convenience it is desired to maintain the length, then augment the beginning element

g=[0;diff(v(:,2))./diff(v(:,1))];       % numerical gradient with initial 0 value

IFF the time steps are uniform, you could instead use

h=diff(v(1:2,1));           % the fixed delta_t
g=[0;gradient(v(:,2)),h];   % numerical gradient with initial 0 value, uniform delta_t

[Shiv Nileshkumar Matliwala]

As you can see, This is the plot of my data set. Now i want to do the differentiation of this curve shown here.

All i know is when we do differentiation of ramp input, we get step input. but i want to do the differentiation into matlab script by writing code.

Here this cruve has 80000 data values.

By using your code what i got is as below. And this is not my expected result.

Can you please help me with this ??

[dpb]

That looks like differential between points is just roundoff...

Attach a .mat file with a sample of your data -- it could be just the first hundred points or so would be enough to find out what's going on.

I'll amend my Answer to agree with @Torsten, however, that gradient is better than the first difference; I had forgotten it uses central differences and not the simple differences that diff does, so will give a smoother estimate that may help. Also, though, it does return a full-length vector automagically so you don't need to augment the front end; just use

g=gradient(v(:,2))./gradient(v(:,1));       % numerical gradient variable sampling

if the time spacing is nonuniform or

g=gradient(v(:,2),h);       % numerical gradient fixed sampling, h

for fixed sample rate.

Answer 2

[Torsten]

B = [A(:,1),gradient(A(:,2))./gradient(A(:,1));
plot(B(:,1),B(:,2))