/// <summary>
/// Performs the transformation over a double[] array.
/// </summary>
public static void FHT(double[] data, FourierTransform.Direction direction)
{
int N = data.Length;
// Forward operation
if (direction == FourierTransform.Direction.Forward)
{
// Copy the input to a complex array which can be processed
// in the complex domain by the FFT
var cdata = new Complex[N];
for (int i = 0; i < N; i++)
{
cdata[i].Re = data[i];
}
// Perform FFT
FourierTransform.FFT(cdata, FourierTransform.Direction.Forward);
//double positive frequencies
for (int i = 1; i < (N / 2); i++)
{
cdata[i].Re *= 2.0;
cdata[i].Im *= 2.0;
}
// zero out negative frequencies
// (leaving out the dc component)
for (int i = (N / 2) + 1; i < N; i++)
{
cdata[i].Re = 0.0;
cdata[i].Im = 0.0;
}
// Reverse the FFT
FourierTransform.FFT(cdata, FourierTransform.Direction.Backward);
// Convert back to our initial double array
for (int i = 0; i < N; i++)
{
data[i] = cdata[i].Im;
}
}
else // Backward operation
{
// The inverse Hilbert can be calculated by
// negating the transform and reapplying the
// transformation.
//
// H^–1{h(t)} = –H{h(t)}
FHT(data, FourierTransform.Direction.Forward);
for (int i = 0; i < data.Length; i++)
{
data[i] = -data[i];
}
}
}
/// <summary>
/// Performs the Fast Hilbert Transform over a complex[] array.
/// </summary>
///
public static void FHT(Complex[] data, FourierTransform.Direction direction)
{
int N = data.Length;
// Forward operation
if (direction == FourierTransform.Direction.Forward)
{
// Makes a copy of the data so we don't lose the
// original information to build our final signal
Complex[] shift = (Complex[])data.Clone();
// Perform FFT
FourierTransform.FFT(shift, FourierTransform.Direction.Backward);
TransformArray(shift);
// Reverse the FFT
FourierTransform.FFT(shift, FourierTransform.Direction.Forward);
// Put the Hilbert transform in the Imaginary part
// of the input signal, creating a Analytic Signal
for (int i = 0; i < N; i++)
{
data[i] = new Complex(data[i].Real, shift[i].Imaginary);
}
}
else // Backward operation
{
// Just discard the imaginary part
for (int i = 0; i < data.Length; i++)
{
data[i] = new Complex(data[i].Real, 0.0);
}
}
}
/// <summary>
/// Two dimensional Fast Fourier Transform.
/// </summary>
///
/// <param name="data">Data to transform.</param>
/// <param name="direction">Transformation direction.</param>
///
/// <remarks><para><note>The method accepts <paramref name="data"/> array of 2<sup>n</sup> size
/// only in each dimension, where <b>n</b> may vary in the [1, 14] range. For example, 16x16 array
/// is valid, but 15x15 is not.</note></para></remarks>
///
/// <exception cref="ArgumentException">Incorrect data length.</exception>
///
public static void FFT2(Complex[,] data, Direction direction)
{
int k = data.GetLength(0);
int n = data.GetLength(1);
// check data size
if (!Tools.IsPowerOf2(k) || !Tools.IsPowerOf2(n))
{
throw new ArgumentException("The matrix rows and columns must be a power of 2.");
}
if (k < minLength || k > maxLength || n < minLength || n > maxLength)
{
throw new ArgumentException("Incorrect data length.");
}
// process rows
var row = new Complex[n];
for (int i = 0; i < k; i++)
{
// copy row
for (int j = 0; j < row.Length; j++)
{
row[j] = data[i, j];
}
// transform it
FourierTransform.FFT(row, direction);
// copy back
for (int j = 0; j < row.Length; j++)
{
data[i, j] = row[j];
}
}
// process columns
var col = new Complex[k];
for (int j = 0; j < n; j++)
{
// copy column
for (int i = 0; i < k; i++)
{
col[i] = data[i, j];
}
// transform it
FourierTransform.FFT(col, direction);
// copy back
for (int i = 0; i < k; i++)
{
data[i, j] = col[i];
}
}
}
/// <summary>
/// Performs the transformation over a complex[] array.
/// </summary>
public static void FHT(Complex[] data, FourierTransform.Direction direction)
{
int N = data.Length;
// Forward operation
if (direction == FourierTransform.Direction.Forward)
{
// Makes a copy of the data so we don't lose the
// original information to build our final signal
var shift = (Complex[])data.Clone();
// Perform FFT
FourierTransform.FFT(shift, FourierTransform.Direction.Backward);
//double positive frequencies
for (int i = 1; i < (N / 2); i++)
{
shift[i].Re *= 2.0;
shift[i].Im *= 2.0;
}
// zero out negative frequencies
// (leaving out the dc component)
for (int i = (N / 2) + 1; i < N; i++)
{
shift[i].Re = 0.0;
shift[i].Im = 0.0;
}
// Reverse the FFT
FourierTransform.FFT(shift, FourierTransform.Direction.Forward);
// Put the Hilbert transform in the Imaginary part
// of the input signal, creating a Analytic Signal
for (int i = 0; i < N; i++)
{
data[i].Im = shift[i].Im;
}
}
else // Backward operation
{
// Just discard the imaginary part
for (int i = 0; i < data.Length; i++)
{
data[i].Im = 0.0;
}
}
}
/// <summary>
/// Performs the Fast Hilbert Transform over a double[] array.
/// </summary>
///
public static void FHT(double[] data, FourierTransform.Direction direction)
{
int N = data.Length;
// Forward operation
if (direction == FourierTransform.Direction.Forward)
{
// Copy the input to a complex array which can be processed
// in the complex domain by the FFT
Complex[] cdata = new Complex[N];
for (int i = 0; i < N; i++)
{
cdata[i] = new Complex(data[i], 0.0);
}
// Perform FFT
FourierTransform.FFT(cdata, FourierTransform.Direction.Forward);
TransformArray(cdata);
// Reverse the FFT
FourierTransform.FFT(cdata, FourierTransform.Direction.Backward);
// Convert back to our initial double array
for (int i = 0; i < N; i++)
{
data[i] = cdata[i].Imaginary;
}
}
else // Backward operation
{
// The inverse Hilbert can be calculated by
// negating the transform and reapplying the
// transformation.
//
// H^–1{h(t)} = –H{h(t)}
FHT(data, FourierTransform.Direction.Forward);
for (int i = 0; i < data.Length; i++)
{
data[i] = -data[i];
}
}
}
/// <summary>
/// One dimensional Fast Fourier Transform.
/// </summary>
///
/// <param name="data">Data to transform.</param>
/// <param name="direction">Transformation direction.</param>
///
/// <remarks><para><note>The method accepts <paramref name="data"/> array of 2<sup>n</sup> size
/// only, where <b>n</b> may vary in the [1, 14] range.</note></para></remarks>
///
/// <exception cref="ArgumentException">Incorrect data length.</exception>
///
public static void FFT(Complex[] data, Direction direction)
{
int n = data.Length;
int m = Tools.Log2(n);
// reorder data first
ReorderData(data);
// compute FFT
int tn = 1, tm;
for (int k = 1; k <= m; k++)
{
Complex[] rotation = FourierTransform.GetComplexRotation(k, direction);
tm = tn;
tn <<= 1;
for (int i = 0; i < tm; i++)
{
Complex t = rotation[i];
for (int even = i; even < n; even += tn)
{
int odd = even + tm;
Complex ce = data[even];
Complex co = data[odd];
double tr = co.Real * t.Real - co.Imaginary * t.Imaginary;
double ti = co.Real * t.Imaginary + co.Imaginary * t.Real;
data[even] += new Complex(tr, ti);
data[odd] = new Complex(ce.Real - tr, ce.Imaginary - ti);
}
}
}
if (direction == Direction.Forward)
{
for (int i = 0; i < data.Length; i++)
{
data[i] /= (double)n;
}
}
}