Discrete derivative via Matlab

Hi to all,

I have tried to derivative a simple sine function with diff.

Here are the code:

x = 0:pi/100:10*pi;
y = sin(x);
figure;
plot(y)
y1 = diff(y);
figure;
plot(y1)

The question is this: why the derivative (a cosine function) isn't with max and min of 1 and -1 like sin(x)?

If I do:

Y1=max(y1);
Y=max(y);
Scale = Y/Y1

I obtain Scale = 31.8362.

The same is for second derivative: to obtain function in scale I must apply Scale factor two times.

Who can explain me the correct way to obtain a discrete derivative via Matlab?

Answer 1

[Laurent]

If you want to calculate the derivative like this, you have to divide the change in y (dy) by the change in x (dx), so dy/dx. You get the dy's by running the 'diff' command. The dx is equal to the distance between your x-values, in this case pi/100.

So in your case:

y1=diff(y)/(pi/100);

[Giacomo Alessandroni]

Thank you very much.

Now I write the correct code for all:

dx = pi/100;
x = 0:dx:10;
y = sin(x);
% y' = dy/dx
y1 = diff(y)/dx;
plot(x(1:end-1), y(1:end-1), x(1:end-1), y1)