How to get back the values of a curve from its cumulative integral value?

I have a amplitude distribution with time ( i.e. real curve, blak line). Then I did cumulative trapezoidal inegration of the curve using cumtrapz, which is represented by blue curve. Now, I again retain the real curve i.e. black curve from its cumulative integration i.e. blue curve. How I will get the real curve? Please provide me the suggestions. Thanks in advance.

Answer 1

[darova]

Use diff to find real curve from cumulative trapezoid result

[AS]

it is only showing zero values after applying diff.

[AS]

real curve in not returned.

[darova]

See this

x = 0:0.1:10;
y = x.*sin(x);              % original data
inty = cumtrapz(x,y);       % integrated data
y1 = diff(inty)./diff(x);   % return data
plot(x,y,'k')
line(x,inty,'color','r')
line(x(2:end),y1)
legend('original','integra','returned')

[AS]

Thank you so much for your clarification. But, in my problem it is not working. I have a matrix with dimension 64 by 1, where 1st column is having amplitude values (attached). Now, I am doing cumtrapz to obtain integral value and then did diff to retain original values. But, i am not getting the exact values as original. Could you please check it once.

[darova]

Works ok for me

clc,clear

y = load('data.txt');
x = 1:length(y);
inty = cumtrapz(x,y);
y1 = diff(inty)./diff(x);
plot(x,y,'r')
line(x,inty,'color','k','linestyle','--')
line(x(2:end),y1)
legend('original','returned')

[AS]

Thank you so much. I did mistake in length of the data. Now it is appropiate. Thanks a lot.