# Autocorrelation of a vector series (2)

The given C# source code computes the autocorrelation of a vector series using a Fast Fourier Transform.

Can you review this code for correctness?

using System;
using System.Collections.Generic;
using System.Numerics;

public class TimeSeriesAnalysisForVectors
{
private static Complex[] FFT(Complex[] x)
{
int n = x.Length;
if (n == 1)
return new Complex[] { x[0] };

Complex[] even = new Complex[n / 2];
Complex[] odd = new Complex[n / 2];
for (int i = 0; i < n / 2; i++)
{
even[i] = x[2 * i];
odd[i] = x[2 * i + 1];
}

Complex[] evenTransformed = FFT(even);
Complex[] oddTransformed = FFT(odd);

Complex[] result = new Complex[n];
for (int i = 0; i < n / 2; i++)
{
double angle = -2 * Math.PI * i / n;
Complex twiddle = Complex.FromPolarCoordinates(1, angle);
result[i] = evenTransformed[i] + twiddle * oddTransformed[i];
result[i + n / 2] = evenTransformed[i] - twiddle * oddTransformed[i];
}

return result;
}

private static Complex[] FourierTransform(List<Vec3> vectors)
{
int n = vectors.Count;
Complex[] fftInput = new Complex[n];

for (int i = 0; i < n; i++)
{
fftInput[i] = new Complex(vectors[i].X, 0);
}

// Compute FFT
return FFT(fftInput);
}

private static List<double> ComputeAutoCorrelation(Complex[] fftInput)
{
int n = fftInput.Length;
List<double> autoCorrelations = new List<double>();

// Compute auto-correlation using the FFT result
for (int i = 0; i < n; i++)
{
}

return autoCorrelations;
}

public static List<double> GetAutoCorrelationPoints(List<Vec3> vectors, int maxLag)
{
var fftInput = FourierTransform(vectors);
var autoCorrelations = ComputeAutoCorrelation(fftInput);

// Extract autocorrelation values up to maxLag
var result = new List<double>();
for (int lag = 0; lag <= maxLag && lag < autoCorrelations.Count; lag++)
{