public static List <complex> ForwardDiscreteFourierTransform(List <complex> Signal)
{
int N = Signal.Count;
List <complex> OutSignal = new List <complex>();
for (int i = 0; i < N; i++)
{
OutSignal.Add(new complex(0));
for (int j = 0; j < N; j++)
{
var w = ComplexConverter.FromRadians(1, (-2 * Math.PI * i * j) / N);
OutSignal[i] += w * Signal[j];
}
}
return(OutSignal);
}
public static List <complex> InverseFourierTransform(List <complex> Signal)
{
if (Signal.Count == 1)
{
return(Signal);
}
var N = Signal.Count;
var Even = Signal.Where((item, index) => index % 2 == 0).ToList();
var Odd = Signal.Where((item, index) => index % 2 != 0).ToList();
var yEven = ForwardFourierTransform(Even);
var yOdd = ForwardFourierTransform(Odd);
var Y = new List <complex>();
for (int i = 0; i < N; i++)
{
Y.Add(new complex(0, 0));
}
var W = new List <complex>();
for (int i = 0; i < N; i++)
{
double alpha = 2 * Math.PI * i / N;
W.Add(ComplexConverter.FromRadians(1, alpha));
}
for (int i = 0; i < N / 2; i++)
{
Y[i] = (yEven[i] + W[i] * yOdd[i]) / N;
Y[i + N / 2] = (yEven[i] - W[i] * yOdd[i]) / N;
}
return(Y);
}