How to integrate (find the antiderivative) of a digital signal in C++?

Question

C++ / C#

There is a signal represented as an array of values, a sample rate (or period), and a timestamp. You need to integrate it. The formula as in the link doesn't help much.
Who knows how it's done?

Answer 1

The materiel is here vunivere.ru/work10048 It looks like what you need.
And another discrete primitive studopedia.info/1-113131.html

class Antiderivative
{
private: //variables
  //size_t isize;  /// период интегрирования, TODO орраничеение периода (динамический кольцевой буффер)
  float XN=0;      /// накопленная сумма-первообразная
public:
    void count( float in[], size_t len, float out[] ){
        //X[k] - X[N] = sum(i=N,i<k)x[i];
        for( size_t i=0; i<len; ++i ){
            out[i] = count(in[i]);
         }
    } 
  /// считает одно значение
  float count( float in ){
                float ret = XN;
    XN += in;
    return ret;
  }
};

I quickly built a project in Qt with visualization for verification, if someone needs to find it, I'll post it.
Updated. If there is another option for integrating a signal based on an alpha-beta filter (simplified Kalman). At the end, he did it.

Answer 2

It will not work to integrate here, since the signal is finite, but for integration, give an infinite one.
If you want to get the spectrum of a signal in the frequency domain, then you need the Fast Fourier Transform (FFT). You can start here: www.fftw.org
Many math libraries have implementations, such as the Intel Math Kernel Library.