fourier c++

/*by
Kostanski Grzegorz

*/
#include <iostream>
#include <complex>
#include <math.h>
#include <vector>
#include <iomanip>
#include <valarray>
#define USE MATH DEFINES
const double M_PI = acos(-1);
using namespace std;
typedef complex<double> Complex;
typedef valarray<Complex> CArray;
//const complex<double> I(0, 1);

vector<Complex> createSignal(){
    int N = 8;
    vector<Complex> signal;
    signal.reserve(N);
    double sigK = 3.0;
    double sigPhase = M_PI / 4.0;
    for (int x = 0; x < N; x++) {
        auto currentSample = Complex(cos((2 * M_PI / static_cast<double>(N)) * sigK * static_cast<double>(x) + sigPhase), 0.0);
        signal.push_back(currentSample);
    }
    return signal;
}

CArray convertSignal(vector<Complex> x){
    int n = x.size();
    CArray data(n);
    for (int i = 0; i < n; i++) {
        data[i] = x[i];
    }
    return data;
}

vector<Complex> dft(vector<Complex> x) {
    int n = x.size(); int k = n;
    Complex intSum;
    vector<Complex> output;
    output.reserve(k);
    for (int i = 0; i < k; i++) {
        intSum = Complex(0, 0);
        for (int j = 0; j < n; j++) {
            double real = cos(((2 * M_PI) / n) * i * j);
            double imag = sin(((2 * M_PI) / n) * i * j);
            Complex w(real, imag);
            intSum += x[j] * w;
        }
        output.push_back(intSum);
    }
    return output;
}

CArray fft(CArray& x){
    const size_t N = x.size();
    if (N <= 1) return x;
    // divide
    CArray even = x[slice(0, N / 2, 2)];
    CArray  odd = x[slice(1, N / 2, 2)];
    fft(even);
    fft(odd);
    for (size_t k = 0; k < N / 2; ++k){    // combine
        Complex t = polar(1.0, -2 * M_PI * k / N) * odd[k];
        x[k] = even[k] + t;
        x[k + N / 2] = even[k] - t;
    }
    return x;
}

double repair(double N) { //returns 2**x number
    double logr = log2(N);
    logr = int(logr);
    return pow(2, logr);
}

int main()
{
    vector<Complex> syg = createSignal();
    CArray csig = convertSignal(syg);
    syg = dft(syg);
    csig = fft(csig);
    cout << "dft" << endl;
    for (int i = 0; i < 8; i++) {
        cout << syg[i] << endl;
    }

    cout << "fft" << endl;

    for (int i = 0; i < 8; i++) {
        cout << csig[i] << endl;
    }


return 1;
}