Help on derivative of a function in discrete time

Hello all Please can you help me out calculating derivatives of discrete time functions in matlab r(k+1) from r(k)

Given a discrete signal r(k)=0.5*sin*(pi*k*ts) for k=1:1=100

I found in one book that they used an extrapolation method as follows:

   dr(k)=(r(k)-r_1)/ts;
   dr_1=(r_1-r_2)/ts;
   r1(k)=2*r(k)-r_1;
   dr1(k)=2*dr(k)-dr_1;

to calculate first and second derivatives. i didn't understand this method

I tried rather to use a simple formula:

    r_1=0;
    r_1(k)=r(k)-r_1/ts;
    r_1=r(k);

I don't know if this is correct ?

Thank you so much for your precious help

Best regards

Answer 1

[Walter Roberson]

You change the same variable in all three lines. You have

    r_1=0;
    r_1(k)=r(k)-r_1/ts;
    r_1=r(k);

You set all of r_1 in the first line. In the second line you overwrite only part of r_1 . But in the third line you overwrite all of it, using a value that was not changed in the previous lines. The effect is going to be as if you had only one line

r_1 = r(k);

I cannot really advise on the correctness of the method you showed from the book as I do not know what r1 is intended to represent that is different from dr. Also we would need to know how r_1 and r_2 are initialized. My suspicion is that the book might also show them changing, possibly like

r_2 = r_1;
r_1 = r(k);

so that the variables represent the two previous values.

[lady bird]

Thank you Walter Roberson for your answer

in fact, i did a mistake my code was rather as follows:

    r_1=0;
    r1(k)=r(k)-r_1/ts;
    r_1=r(k); 

where r1(k) is the first derivative, and i dont know if this is correct

In the other hand, yes i just checked in that book , there is an update of the variables as u just stated

   r_2 = r_1;
   r_1 = r(k);

r_1 and r_2 are initialized to zero at first

[lady bird]

Thank you Walter Roberson for your answer

in fact, i did a mistake my code was rather as follows:

    r_1=0;
    r1(k)=r(k)-r_1/ts;
    r_1=r(k); 

where r1(k) is the first derivative, and i dont know if this is correct

In the other hand, yes i just checked in that book , there is an update of the variables as u just stated

   r_2 = r_1;
   r_1 = r(k);

r_1 and r_2 are initialized to zero at first

[Walter Roberson]

They are using dr() as the first derivative, it appears, so I do not understand why they would also have r1.

The r_1 and r_2 make sense to me now.