/// <summary>
/// Calculate the Haar forward fast wavelet transform in 1-dimension.
/// </summary>
/// <param name="signal">Signal to compute (must be power two)</param>
public static void Haar_forward_FWT_1d(ref double[] signal)
{
int m;
int npts;
npts = (int)DSPUtilities.NextPowerOfTwo((int)signal.Length);
for (m = signal.Length - 1; m >= 0; m--)
{
Wavelet.Haar_forward_pass_1d(m + 1, ref signal);
//Wavelet.Haar_ip_FFWT_1d(m + 1, ref signal);
}
/*int i = 0;
* int w = signal.Length;
* double[] vecp = new double[signal.Length];
* for (i = 0; i < signal.Length; i++)
* vecp[i] = 0;
* //while (w > 1)
* // {
* w /= 2;
* for (i = 0; i < w; i++)
* {
* vecp[i] = (signal[2 * i] + signal[2 * i + 1]) / Math.Sqrt(2.0);
* vecp[i + w] = (signal[2 * i] - signal[2 * i + 1]) / Math.Sqrt(2.0);
* }
* for (i = 0; i < (w * 2); i++)
* signal[i] = vecp[i];
* // }*/
}
/// <summary>
/// Calculate one iteration of the Haar inverse FWT in 2-dimensions.
/// </summary>
/// <param name="signal">Signal to compute (must be power two)</param>
/* static void Haar_inverse_pass_2d(int n, ref double[][] signal)
* {
* int i, j;
* int npts;
*
* npts = (int) Utilities.NextPowerOfTwo((int) n);
* for (i = 0; i < npts; i++)
* {
* Wavelet.Haar_inverse_pass_1d(n, ref signal[i]);
* }
* double[] c = new double[npts];
* for (j = 0; j < npts; j++)
* {
* for (i = 0; i < npts; i++)
* c[i] = signal[i][j];
* Wavelet.Haar_inverse_pass_1d(n, ref c);
* for (i = 0; i < npts; i++)
* signal[i][j] = c[i];
* }
* }*/
/// <summary>
/// Calculate the Haar inverse fast wavelet transform in 2-dimensions.
/// </summary>
/// <param name="signal">Signal to compute (must be power two)</param>
public static void Haar_inverse_FWT_2d(int width, int height, ref double[] signal)
{
/*for (int m = 1; m <= signal.Length; m++)
* {
* Haar_inverse_pass_2d(m, ref signal);
* }*/
double[] row = new double[DSPUtilities.NextPowerOfTwo((int)width)];
double[] column = new double[DSPUtilities.NextPowerOfTwo((int)height)];
for (int x = 0; x < width; x++)
{
for (int y = 0; y < height; y++)
{
column[y] = signal[x + (y * width)];
}
Wavelet.Haar_inverse_FWT_1d(ref column);
for (int y = 0; y < height; y++)
{
signal[x + (y * width)] = column[y];
}
}
for (int y = 0; y < height; y++)
{
Array.Copy(signal, (int)(y * width), row, 0, (int)width);
Wavelet.Haar_inverse_FWT_1d(ref row);
Array.Copy(row, 0, signal, (int)(y * width), (int)width);
}
}
/// <summary>
/// Calculate Haar in-place inverse fast wavelet transform in 1-dimension.
/// </summary>
/// <param name="n">Elements to compute</param>
/// <param name="signal">Signal to compute (must be power two)</param>
static void Haar_ip_IFWT_1d(int n, ref double[] signal)
{
double a0;
double a1;
int i;
int j;
int k;
int l;
int m;
i = (int)DSPUtilities.NextPowerOfTwo((int)(n - 1));
j = 2 * i;
m = 1;
for (l = 1; l <= n; l++)
{
//System.Diagnostics.Debug.WriteLine("l = " + l);
for (k = 0; k < m; k++)
{
a0 = signal[j * k] + signal[j * k + i];
a1 = signal[j * k] - signal[j * k + i];
signal[j * k] = a0;
signal[j * k + i] = a1;
}
i /= 2;
j /= 2;
m *= 2;
}
}
// Haar Wavelet
/// <summary>
/// Calculate Haar in-place forward fast wavelet transform in 1-dimension.
/// </summary>
/// <param name="n">Elements to compute</param>
/// <param name="signal">Signal to compute</param>
static void Haar_ip_FFWT_1d(int n, ref double[] signal)
{
double a;
double c;
int i;
int j;
int k;
int l;
int m;
i = 1;
j = 2;
m = (int)DSPUtilities.NextPowerOfTwo((int)n);
for (l = n - 1; l >= 0; l--)
{
//System.Diagnostics.Debug.WriteLine("l = " + l);
m /= 2;
for (k = 0; k < m; k++)
{
a = (signal[j * k] + signal[j * k + i]) / 2.0;
c = (signal[j * k] - signal[j * k + i]) / 2.0;
signal[j * k] = a;
signal[j * k + i] = c;
}
i *= 2;
j *= 2;
}
}
/// <summary>
/// Calculate one iteration of the Haar inverse FWT in 1-dimension.
/// </summary>
/// <param name="n">Elements to compute</param>
/// <param name="signal">Signal to compute (must be power two)</param>
static void Haar_inverse_pass_1d(int n, ref double[] signal)
{
int i;
int npts = (int)DSPUtilities.NextPowerOfTwo((int)n);
double[] r = new double[npts];
for (i = 0; i < npts / 2; i++)
{
r[2 * i] = signal[i] + signal[i + npts / 2];
r[2 * i + 1] = signal[i] - signal[i + npts / 2];
}
for (i = 0; i < npts; i++)
{
signal[i] = r[i];
}
}
/// <summary>
/// Calculate one iteration of the Haar forward FWT in 1-dimension.
/// </summary>
/// <param name="n">Elements to compute</param>
/// <param name="signal">Signal to compute (must be power two)</param>
static void Haar_forward_pass_1d(int n, ref double[] signal)
{
int i;
int npts;
npts = (int)DSPUtilities.NextPowerOfTwo((int)n);
double[] a = new double[npts / 2];
double[] c = new double[npts / 2];
for (i = 0; i < npts / 2; i++)
{
a[i] = (signal[2 * i] + signal[2 * i + 1]) / 2.0;
c[i] = (signal[2 * i] - signal[2 * i + 1]) / 2.0;
}
for (i = 0; i < npts / 2; i++)
{
signal[i] = a[i];
signal[i + npts / 2] = c[i];
}
}
/// <summary>
/// Compute FFT
/// </summary>
/// <param name="NumSamples">NumSamples Number of samples (must be power two)</param>
/// <param name="pRealIn">Real samples</param>
/// <param name="pImagIn">Imaginary (optional, may be null)</param>
/// <param name="pRealOut">Real coefficient output</param>
/// <param name="pImagOut">Imaginary coefficient output</param>
/// <param name="bInverseTransform">bInverseTransform when true, compute Inverse FFT</param>
public static void Compute(int NumSamples, IEnumerable <double> pRealIn, Double[] pImagIn,
Double[] pRealOut, Double[] pImagOut, Boolean bInverseTransform)
{
int NumBits; /* Number of bits needed to store indices */
int i, j, k, n;
int BlockSize, BlockEnd;
double angle_numerator = 2.0 * DSPUtilities.DDC_PI;
double tr, ti; /* temp real, temp imaginary */
if (pRealIn == null || pRealOut == null || pImagOut == null)
{
// error
throw new ArgumentNullException("Null argument");
}
if (!DSPUtilities.IsPowerOfTwo((int)NumSamples))
{
// error
throw new ArgumentException("Number of samples must be power of 2");
}
if (pRealIn.Count() < NumSamples || (pImagIn != null && pImagIn.Length < NumSamples) ||
pRealOut.Length < NumSamples || pImagOut.Length < NumSamples)
{
// error
throw new ArgumentException("Invalid Array argument detected");
}
if (bInverseTransform)
{
angle_numerator = -angle_numerator;
}
NumBits = NumberOfBitsNeeded(NumSamples);
/*
** Do simultaneous data copy and bit-reversal ordering into outputs...
*/
for (i = 0; i < NumSamples; i++)
{
j = ReverseBits(i, NumBits);
pRealOut[j] = pRealIn.ElementAt(i);
pImagOut[j] = (double)((pImagIn == null) ? 0.0 : pImagIn[i]);
}
/*
** Do the FFT itself...
*/
BlockEnd = 1;
for (BlockSize = 2; BlockSize <= NumSamples; BlockSize <<= 1)
{
double delta_angle = angle_numerator / (double)BlockSize;
double sm2 = Math.Sin(-2 * delta_angle);
double sm1 = Math.Sin(-delta_angle);
double cm2 = Math.Cos(-2 * delta_angle);
double cm1 = Math.Cos(-delta_angle);
double w = 2 * cm1;
double ar0, ar1, ar2;
double ai0, ai1, ai2;
for (i = 0; i < NumSamples; i += BlockSize)
{
ar2 = cm2;
ar1 = cm1;
ai2 = sm2;
ai1 = sm1;
for (j = i, n = 0; n < BlockEnd; j++, n++)
{
ar0 = w * ar1 - ar2;
ar2 = ar1;
ar1 = ar0;
ai0 = w * ai1 - ai2;
ai2 = ai1;
ai1 = ai0;
k = j + BlockEnd;
tr = ar0 * pRealOut[k] - ai0 * pImagOut[k];
ti = ar0 * pImagOut[k] + ai0 * pRealOut[k];
pRealOut[k] = (pRealOut[j] - tr);
pImagOut[k] = (pImagOut[j] - ti);
pRealOut[j] += (tr);
pImagOut[j] += (ti);
}
}
BlockEnd = BlockSize;
}
/*
** Need to normalize if inverse transform...
*/
if (bInverseTransform)
{
double denom = (double)(NumSamples);
for (i = 0; i < NumSamples; i++)
{
pRealOut[i] /= denom;
pImagOut[i] /= denom;
}
}
}