how to implement the integral formula in Matlab ?

The question says all. The formula is to compute energy of the signal given by

I have computed D(f)

it is the fft spectrum of my time domain signal. How to implement this formula (ER) in Matlab?

As I know maths the value of an integral will be one value, but in the paper I referred according to the author the result is similar to spectrum but different values.

Answer 1

[Walter Roberson]

Fft of a finite length signal is a discrete process so the output cannot be integrated unless you do numeric integration with trapz or similar.

If you had a theoretically infinite signal then potentially you could do a continuous fourier transform and integrate that.

[Raady]

The signal is of finite length. how can we perform that integration then?

[Walter Roberson]

You cannot do an integration of a discrete system.

You could use trapz() but make sure you get the x coordinates correct, and watch out for the fact that the results of fft include negative and positive frequency components. Watch out too for whether you are integrating only the real components or if you are doing a complex integration