/// <summary>
/// Forward Hilbert transform.
/// </summary>
/// <param name="A">Array</param>
/// <returns>Array</returns>
public Complex32[] Forward(Complex32[] A)
{
int N = A.Length;
Complex32[] F = FFT.Forward(A);
HilbertTransform.hilbertf(F, N);
F = FFT.Backward(F);
return(HilbertTransform.hilbertb(A, F, N));
}
/// <summary>
/// Backward cosine transform.
/// </summary>
/// <param name="B">Array</param>
/// <returns>Array</returns>
public float[] Backward(float[] B)
{
int N = B.Length, N2 = N / 2, i, k;
Complex32[] A = new Complex32[N];
Complex32 c = Maths.I * Maths.Pi / (2 * N);
for (k = 0; k < N; k++)
{
A[k] = B[k] * Maths.Exp(c * k) * Math.Sqrt(2 * N);
}
A[0] /= Math.Sqrt(2); // DCT-I
A = FFT.Backward(A);
float[] C = new float[N];
for (i = 0; i < N2; i++)
{
var j = 2 * i;
C[j] = A[i].Real / N;
C[j + 1] = A[N - i - 1].Real / N;
}
return(C);
}
/// <summary>
/// Backward cosine transform.
/// </summary>
/// <param name="B">Array</param>
/// <returns>Array</returns>
public float[] Backward(float[] B)
{
int N = B.Length, N2 = N * 2, i, k;
Complex32[] A = new Complex32[N2];
float Bk, temp, c = Maths.Pi / N;
for (k = 0; k < N; k++)
{
Bk = B[k];
temp = k * c;
A[k] = new Complex32(Bk * (float)Math.Cos(temp), Bk * (float)Math.Sin(temp));
}
A = FFT.Backward(A);
float[] C = new float[N];
for (i = 0; i < N; i++)
{
C[i] = -A[i].Imag * 2.0f;
}
C[N - 1] = B[0] * Maths.Sqrt2;
return(C);
}
/// <summary>
/// Backward Hartley transform.
/// </summary>
/// <param name="B">Array</param>
/// <returns>Array</returns>
public float[] Backward(float[] B)
{
Complex32[] A = Matrice.ToComplex(B);
A = FFT.Backward(A);
int length = B.Length, i;
float[] Hk = new float[length];
for (i = 0; i < length; i++)
{
Hk[i] = A[i].Real + A[i].Imag;
}
return(Hk);
}
/// <summary>
/// Backward Laplace transform.
/// </summary>
/// <param name="B">Array</param>
/// <returns>Array</returns>
public Complex32[] Backward(Complex32[] B)
{
// Laplace to Fourier transform:
Complex32[] A = (Complex32[])B.Clone();
invlaplace(A, sigma);
// Fourier transform:
return(FFT.Backward(A));
}
