#include <iostream>
#include <cstdlib>
#include <ctime>
#include <cmath>
#include <fstream>
#include <string>
#include <complex>
#include <vector>


using namespace std;

double signal(double t, double T)
{
    const double A = 1.0;
    const double f = 20.0;
    const double phi = M_PI / 2;

    return A * sin(2.0 * M_PI * f * t + phi);
}

double* generateSignal(int T)
{
    auto tabSignal = new double[T];

    for (int i = 0; i < T; i++) {
        tabSignal[i] = i / (double) T;
    }

    return tabSignal;
}

vector<double> dff(double* signal, int N)
{
    vector<double> results;

    for (int i = 0; i < N / 2; i++) {
        complex<double> sum = 0;

        complex<double> e(cos(-2 * M_PI * i / N), sin(-2 * M_PI * i / N));
        for (int j = 0; j < N; j++) {
            complex<double> x1(cos(-2 * M_PI * i * j / N), sin(-2 * M_PI * i * j / N));

            x1 = signal[j] * x1;

            sum += x1;
        }

        results.push_back(abs(sum));
    }

    return results;
}

vector<double> fft(double* signal, int N)
{
    vector<double> results;

    for (int i = 0; i < N / 2; i++) {
        complex<double> sum1 = 0;
        complex<double> sum2 = 0;

        complex<double> e(cos(-2 * M_PI * i / N), sin(-2 * M_PI * i / N));
        for (int j = 0; j < N / 2; j++) {
            double k = i;
            double n = 2 * j;

            complex<double> x(cos(-2 * M_PI * k * n / N), sin(-2 * M_PI * k * n / N));

            x = signal[(int) n] * x;

            sum1 = sum1 + x;
        }

        for (int j = 0; j < N / 2; j++) {
            double k = i;
            double n = 2 * j + 1;

            complex<double> x(cos(-2 * M_PI * k * n  / N), sin(-2 * M_PI * k * n / N));
            x = signal[(int) n] * x;

            sum2 = sum2 + x;
        }

        results.push_back(abs(sum1) + abs(e * sum2));
    }

    return results;
}

void signalToFile(const string& filePath, double* signal, int N)
{
    fstream file(filePath, ios::out);

    if (!file.good()) {
        cerr << "ERROR: Cannot write to file " << filePath << endl << endl;
        return;
    }

    for (int i = 0; i < N; i++) {
        file << signal[i] << endl;
    }

    file.close();
}

void signalToFile(const string& filePath, vector<double>& signal)
{
    fstream file(filePath, ios::out);

    if (!file.good()) {
        cerr << "ERROR: Cannot write to file " << filePath << endl << endl;
        return;
    }

    for (auto & it : signal) {
        file << fixed << it << endl;
    }

    file.close();
}

int main()
{
    int T = 1000;

    double* signal = generateSignal(T);
    vector<double> fftSpectrum = fft(signal, T);

    signalToFile("signal.txt", signal, T);
    signalToFile("spectrum.txt", fftSpectrum);

    delete[] signal;
}