TransformBackward(
Complex[] samples,
params int[] dimensionLengths
)
{
for (int i = 0; i < dimensionLengths.Length; i++)
{
if (Fn.CeilingToPowerOf2(dimensionLengths[i]) != dimensionLengths[i])
{
throw new ArgumentException(Resources.ArgumentPowerOfTwoEveryDimension, "dimensionLengths");
}
}
double[] samplePairs = new double[samples.Length << 1];
for (int i = 0, j = 0; i < samples.Length; i++, j += 2)
{
samplePairs[j] = samples[i].Real;
samplePairs[j + 1] = samples[i].Imag;
}
_fft.DiscreteFourierTransformMultiDim(samplePairs, dimensionLengths, false, _convention);
for (int i = 0, j = 0; i < samples.Length; i++, j += 2)
{
samples[i].Real = samplePairs[j];
samples[i].Imag = samplePairs[j + 1];
}
}
TransformForward(
double[] samples,
out double[] fftReal,
out double[] fftImag,
params int[] dimensionLengths)
{
for (int i = 0; i < dimensionLengths.Length; i++)
{
if (Fn.CeilingToPowerOf2(dimensionLengths[i]) != dimensionLengths[i])
{
throw new ArgumentException(Properties.LocalStrings.ArgumentPowerOfTwoEveryDimension, "dimensionLengths");
}
}
/* TODO: Implement real version (at the moment this is just a wrapper to the complex version)! */
double[] samplePairs = new double[samples.Length << 1];
for (int i = 0, j = 0; i < samples.Length; i++, j += 2)
{
samplePairs[j] = samples[i];
}
_fft.DiscreteFourierTransformMultiDim(samplePairs, dimensionLengths, true, _convention);
fftReal = new double[samples.Length];
fftImag = new double[samples.Length];
for (int i = 0, j = 0; i < samples.Length; i++, j += 2)
{
fftReal[i] = samplePairs[j];
fftImag[i] = samplePairs[j + 1];
}
}
/// <summary>
/// Outplace Backward Transformation in multiple dimensions.
/// Size must be Power of Two in each dimension.
/// The Data is expected to be ordered such that the last index changes most rapidly (in 2D this means row-by-row when indexing as [y,x]).
/// </summary>
public void TransformBackward(double[] fftReal, double[] fftImag, out double[] samples, params int[] dimensionLengths)
{
if (fftReal.Length != fftImag.Length)
{
throw new ArgumentException(Resources.ArgumentVectorsSameLengths);
}
for (int i = 0; i < dimensionLengths.Length; i++)
{
if (Fn.CeilingToPowerOf2(dimensionLengths[i]) != dimensionLengths[i])
{
throw new ArgumentException(Resources.ArgumentPowerOfTwoEveryDimension, "dimensionLengths");
}
}
// TODO: Implement real version (at the moment this is just a wrapper to the complex version)!
double[] samplePairs = new double[fftReal.Length << 1];
for (int i = 0, j = 0; i < fftReal.Length; i++, j += 2)
{
samplePairs[j] = fftReal[i];
samplePairs[j + 1] = fftImag[i];
}
_fft.DiscreteFourierTransformMultiDim(samplePairs, dimensionLengths, false, _convention);
samples = new double[fftReal.Length];
for (int i = 0, j = 0; i < samples.Length; i++, j += 2)
{
samples[i] = samplePairs[j];
}
}
/// <summary>
/// Inplace Forward Transformation in one dimension. Size must be Power of Two.
/// </summary>
/// <param name="samplePairs">Complex samples (even = real, odd = imaginary). Length must be a power of two.</param>
public void TransformForward(double[] samplePairs)
{
if (Fn.CeilingToPowerOf2(samplePairs.Length) != samplePairs.Length)
{
throw new ArgumentException(Resources.ArgumentPowerOfTwo, "samplePairs");
}
_fft.DiscreteFourierTransform(samplePairs, true, _convention);
}
/// <summary>
/// Outplace Forward Transformation in one dimension for two vectors with the same length.
/// Size must be Power of Two.
/// </summary>
/// <param name="samples1">Real samples. Length must be a power of two.</param>
/// <param name="samples2">Real samples. Length must be a power of two.</param>
public void TransformForward(double[] samples1, double[] samples2,
out double[] fftReal1, out double[] fftImag1, out double[] fftReal2, out double[] fftImag2)
{
if (samples1.Length != samples2.Length)
{
throw new ArgumentException(Resources.ArgumentVectorsSameLengths, "samples2");
}
if (Fn.CeilingToPowerOf2(samples1.Length) != samples1.Length)
{
throw new ArgumentException(Resources.ArgumentPowerOfTwo, "samples1");
}
int numSamples = samples1.Length;
int length = numSamples << 1;
// Pack together to one complex vector
double[] complex = new double[length];
for (int i = 0, j = 0; i < numSamples; i++, j += 2)
{
complex[j] = samples1[i];
complex[j + 1] = samples2[i];
}
// Transform complex vector
_fft.DiscreteFourierTransform(complex, true, _convention);
// Reconstruct data for the two vectors by using symmetries
fftReal1 = new double[numSamples];
fftImag1 = new double[numSamples];
fftReal2 = new double[numSamples];
fftImag2 = new double[numSamples];
double h1r, h2i, h2r, h1i;
fftReal1[0] = complex[0];
fftReal2[0] = complex[1];
fftImag1[0] = fftImag2[0] = 0d;
for (int i = 1, j = 2; j <= numSamples; i++, j += 2)
{
h1r = 0.5 * (complex[j] + complex[length - j]);
h1i = 0.5 * (complex[j + 1] - complex[length + 1 - j]);
h2r = 0.5 * (complex[j + 1] + complex[length + 1 - j]);
h2i = -0.5 * (complex[j] - complex[length - j]);
fftReal1[i] = h1r;
fftImag1[i] = h1i;
fftReal1[numSamples - i] = h1r;
fftImag1[numSamples - i] = -h1i;
fftReal2[i] = h2r;
fftImag2[i] = h2i;
fftReal2[numSamples - i] = h2r;
fftImag2[numSamples - i] = -h2i;
}
}
TransformBackward(double[] samplePairs)
{
if (Fn.CeilingToPowerOf2(samplePairs.Length) != samplePairs.Length)
{
throw new ArgumentException(Properties.LocalStrings.ArgumentPowerOfTwo, "samplePairs");
}
_fft.DiscreteFourierTransform(samplePairs, false, _convention);
}
TransformBackward(
double[] fftReal,
double[] fftImag,
out double[] samples
)
{
if (fftReal.Length != fftImag.Length)
{
throw new ArgumentException(Resources.ArgumentVectorsSameLengths);
}
if (Fn.CeilingToPowerOf2(fftReal.Length) != fftReal.Length)
{
throw new ArgumentException(Resources.ArgumentPowerOfTwo, "samples");
}
int length = fftReal.Length;
int numSamples = length >> 1;
double expSignConvention = (_convention & TransformationConvention.InverseExponent) > 0 ? -1d : 1d;
double theta = -Constants.Pi / numSamples;
double wtemp = Trig.Sine(0.5 * theta);
double wpr = -2.0 * wtemp * wtemp;
double wpi = expSignConvention * Trig.Sine(theta);
double wr = 1.0 + wpr;
double wi = wpi;
samples = new double[length];
double h1r, h2i, h2r, h1i;
// TODO: may be 1 <--> 0 swapped?
samples[1] = 0.5 * (fftReal[0] - fftReal[numSamples]);
samples[0] = 0.5 * (fftReal[0] + fftReal[numSamples]);
for (int i = 1, j = 2; j <= numSamples; i++, j += 2)
{
h1r = 0.5 * (fftReal[i] + fftReal[numSamples - i]);
h1i = 0.5 * (fftImag[i] - fftImag[numSamples - i]);
h2r = -0.5 * (fftImag[i] + fftImag[numSamples - i]);
h2i = 0.5 * (fftReal[i] - fftReal[numSamples - i]);
samples[j] = h1r + wr * h2r + wi * h2i;
samples[j + 1] = h1i + wr * h2i - wi * h2r;
samples[length - j] = h1r - wr * h2r - wi * h2i;
samples[length + 1 - j] = -h1i + wr * h2i - wi * h2r;
wr = (wtemp = wr) * wpr - wi * wpi + wr;
wi = wi * wpr + wtemp * wpi + wi;
}
// Transform odd and even vectors (packed as one complex vector)
_fft.DiscreteFourierTransform(samples, false, _convention);
}
/// <summary>
/// Inplace Backward Transformation in multiple dimensions.
/// Size must be Power of Two in each dimension.
/// The Data is expected to be ordered such that the last index changes most rapidly (in 2D this means row-by-row when indexing as [y,x]).
/// </summary>
/// <param name="samplePairs">Complex samples (even = real, odd = imaginary). Length must be a power of two in each dimension.</param>
public void TransformBackward(double[] samplePairs, params int[] dimensionLengths)
{
for (int i = 0; i < dimensionLengths.Length; i++)
{
if (Fn.CeilingToPowerOf2(dimensionLengths[i]) != dimensionLengths[i])
{
throw new ArgumentException(Resources.ArgumentPowerOfTwoEveryDimension, "dimensionLengths");
}
}
_fft.DiscreteFourierTransformMultiDim(samplePairs, dimensionLengths, false, _convention);
}
public double[] ExtendToPowerOf2Length(double[] samples)
{
int newlen = Fn.CeilingToPowerOf2(samples.Length);
double[] ret = new double[newlen];
for (int i = 0; i < samples.Length; i++)
{
ret[i] = samples[i];
}
// rest is padded with zero.
return(ret);
}
TransformForward(
double[] samplePairs,
params int[] dimensionLengths)
{
for (int i = 0; i < dimensionLengths.Length; i++)
{
if (Fn.CeilingToPowerOf2(dimensionLengths[i]) != dimensionLengths[i])
{
throw new ArgumentException(Properties.LocalStrings.ArgumentPowerOfTwoEveryDimension, "dimensionLengths");
}
}
_fft.DiscreteFourierTransformMultiDim(samplePairs, dimensionLengths, true, _convention);
}
TransformBackward(
double[] fftReal1,
double[] fftImag1,
double[] fftReal2,
double[] fftImag2,
out double[] samples1,
out double[] samples2
)
{
if (fftReal1.Length != fftImag1.Length || fftReal2.Length != fftImag2.Length || fftReal1.Length != fftReal2.Length)
{
throw new ArgumentException(Resources.ArgumentVectorsSameLengths);
}
if (Fn.CeilingToPowerOf2(fftReal1.Length) != fftReal1.Length)
{
throw new ArgumentException(Resources.ArgumentPowerOfTwo, "fftReal1");
}
int numSamples = fftReal1.Length;
int length = numSamples << 1;
// Pack together to one complex vector
double[] complex = new double[length];
for (int i = 0, j = 0; i < numSamples; i++, j += 2)
{
complex[j] = fftReal1[i] - fftImag2[i];
complex[j + 1] = fftImag1[i] + fftReal2[i];
}
// Transform complex vector
_fft.DiscreteFourierTransform(complex, false, _convention);
// Reconstruct data for the two vectors
samples1 = new double[numSamples];
samples2 = new double[numSamples];
for (int i = 0, j = 0; i < numSamples; i++, j += 2)
{
samples1[i] = complex[j];
samples2[i] = complex[j + 1];
}
}
public void TestSpecialFunctions_CeilingToPowerOf2()
{
Assert.That(Fn.CeilingToPowerOf2(0), Is.EqualTo(0), "A");
Assert.That(Fn.CeilingToPowerOf2(1), Is.EqualTo(1), "B");
Assert.That(Fn.CeilingToPowerOf2(2), Is.EqualTo(2), "C");
Assert.That(Fn.CeilingToPowerOf2(3), Is.EqualTo(4), "D");
Assert.That(Fn.CeilingToPowerOf2(4), Is.EqualTo(4), "E");
for (int i = 2; i < 31; i++)
{
int pow = (int)Math.Pow(2.0, i);
Assert.That(Fn.CeilingToPowerOf2(pow), Is.EqualTo(pow), pow.ToString());
Assert.That(Fn.CeilingToPowerOf2(pow - 1), Is.EqualTo(pow), pow.ToString() + "-1");
}
Assert.That(Fn.CeilingToPowerOf2((int.MaxValue >> 1) + 1), Is.EqualTo((int.MaxValue >> 1) + 1), "Y");
Assert.That(Fn.CeilingToPowerOf2((int.MaxValue >> 1)), Is.EqualTo((int.MaxValue >> 1) + 1), "Z");
}
/// <summary>
/// Inplace Backward Transformation in one dimension. Size must be Power of Two.
/// </summary>
/// <param name="samples">Complex samples. Length must be a power of two.</param>
/// <remarks>
/// This method provides a simple shortcut if your data is already available as
/// <see cref="Complex"/> type instances. However, if not, consider using the
/// overloaded method with double pairs instead, it requires less internal copying.
/// </remarks>
public void TransformBackward(Complex[] samples)
{
if (Fn.CeilingToPowerOf2(samples.Length) != samples.Length)
{
throw new ArgumentException(Resources.ArgumentPowerOfTwo, "samplePairs");
}
double[] samplePairs = new double[samples.Length << 1];
for (int i = 0, j = 0; i < samples.Length; i++, j += 2)
{
samplePairs[j] = samples[i].Real;
samplePairs[j + 1] = samples[i].Imag;
}
_fft.DiscreteFourierTransform(samplePairs, false, _convention);
for (int i = 0, j = 0; i < samples.Length; i++, j += 2)
{
samples[i].Real = samplePairs[j];
samples[i].Imag = samplePairs[j + 1];
}
}
TransformForward(Complex[] samples)
{
if (Fn.CeilingToPowerOf2(samples.Length) != samples.Length)
{
throw new ArgumentException(Properties.LocalStrings.ArgumentPowerOfTwo, "samples");
}
double[] samplePairs = new double[samples.Length << 1];
for (int i = 0, j = 0; i < samples.Length; i++, j += 2)
{
samplePairs[j] = samples[i].Real;
samplePairs[j + 1] = samples[i].Imag;
}
_fft.DiscreteFourierTransform(samplePairs, true, _convention);
for (int i = 0, j = 0; i < samples.Length; i++, j += 2)
{
samples[i].Real = samplePairs[j];
samples[i].Imag = samplePairs[j + 1];
}
}
TransformForward(
double[] samples,
out double[] fftReal,
out double[] fftImag)
{
if (Fn.CeilingToPowerOf2(samples.Length) != samples.Length)
{
throw new ArgumentException(Properties.LocalStrings.ArgumentPowerOfTwo, "samples");
}
int length = samples.Length;
int numSamples = length >> 1;
double expSignConvention = (_convention & TransformationConvention.InverseExponent) > 0 ? -1d : 1d;
// Transform odd and even vectors (packed as one complex vector)
// We work on a copy so the original array is not changed.
double[] complex = new double[length];
for (int i = 0; i < complex.Length; i++)
{
complex[i] = samples[i];
}
_fft.DiscreteFourierTransform(complex, true, _convention);
/* Reconstruct data for the two vectors by using symmetries */
double theta = Constants.Pi / numSamples;
double wtemp = Trig.Sine(0.5 * theta);
double wpr = -2.0 * wtemp * wtemp;
double wpi = expSignConvention * Trig.Sine(theta);
double wr = 1.0 + wpr;
double wi = wpi;
fftReal = new double[length];
fftImag = new double[length];
fftImag[0] = fftImag[numSamples] = 0d;
fftReal[0] = complex[0] + complex[1];
fftReal[numSamples] = complex[0] - complex[1];
for (int i = 1, j = 2; j <= numSamples; i++, j += 2)
{
double h1Real = 0.5 * (complex[j] + complex[length - j]);
double h1Imag = 0.5 * (complex[j + 1] - complex[length + 1 - j]);
double h2Real = 0.5 * (complex[j + 1] + complex[length + 1 - j]);
double h2Imag = -0.5 * (complex[j] - complex[length - j]);
fftReal[i] = h1Real + (wr * h2Real) + (wi * h2Imag);
fftImag[i] = h1Imag + (wr * h2Imag) - (wi * h2Real);
fftReal[numSamples - i] = h1Real - (wr * h2Real) - (wi * h2Imag);
fftImag[numSamples - i] = -h1Imag + (wr * h2Imag) - (wi * h2Real);
// For consistency and completeness we also provide the
// negative spectrum, even though it's redundant in the real case.
fftReal[numSamples + i] = fftReal[numSamples - i];
fftImag[numSamples + i] = -fftImag[numSamples - i];
fftReal[length - i] = fftReal[i];
fftImag[length - i] = -fftImag[i];
wr = ((wtemp = wr) * wpr) - (wi * wpi) + wr;
wi = (wi * wpr) + (wtemp * wpi) + wi;
}
}
TransformForward(
double[] samples1,
double[] samples2,
out double[] fftReal1,
out double[] fftImag1,
out double[] fftReal2,
out double[] fftImag2)
{
if (samples1.Length != samples2.Length)
{
throw new ArgumentException(Properties.LocalStrings.ArgumentVectorsSameLengths, "samples2");
}
if (Fn.CeilingToPowerOf2(samples1.Length) != samples1.Length)
{
throw new ArgumentException(Properties.LocalStrings.ArgumentPowerOfTwo, "samples1");
}
int numSamples = samples1.Length;
int length = numSamples << 1;
/* Pack together to one complex vector */
double[] complex = new double[length];
for (int i = 0, j = 0; i < numSamples; i++, j += 2)
{
complex[j] = samples1[i];
complex[j + 1] = samples2[i];
}
/* Transform complex vector */
_fft.DiscreteFourierTransform(complex, true, _convention);
/* Reconstruct data for the two vectors by using symmetries */
fftReal1 = new double[numSamples];
fftImag1 = new double[numSamples];
fftReal2 = new double[numSamples];
fftImag2 = new double[numSamples];
fftReal1[0] = complex[0];
fftReal2[0] = complex[1];
fftImag1[0] = fftImag2[0] = 0d;
for (int i = 1, j = 2; j <= numSamples; i++, j += 2)
{
double h1Real = 0.5 * (complex[j] + complex[length - j]);
double h1Imag = 0.5 * (complex[j + 1] - complex[length + 1 - j]);
double h2Real = 0.5 * (complex[j + 1] + complex[length + 1 - j]);
double h2Imag = -0.5 * (complex[j] - complex[length - j]);
fftReal1[i] = h1Real;
fftImag1[i] = h1Imag;
fftReal1[numSamples - i] = h1Real;
fftImag1[numSamples - i] = -h1Imag;
fftReal2[i] = h2Real;
fftImag2[i] = h2Imag;
fftReal2[numSamples - i] = h2Real;
fftImag2[numSamples - i] = -h2Imag;
}
}
