math.fourierTransforms.interleaved
Class RealDoubleFFT_Radix2

java.lang.Object
  math.fourierTransforms.interleaved.RealDoubleFFT
      math.fourierTransforms.interleaved.RealDoubleFFT_Radix2

public class RealDoubleFFT_Radix2
extends RealDoubleFFT

Computes FFT's of real, double precision data where n is an integral power of 2. The physical layout of the mathematical data d[i] in the array data is as follows:

    d[i] = data[i0 + stride*i]

The FFT (D[i]) of real data (d[i]) is complex, but restricted by symmetry:

    D[n-i] = conj(D[i])

It turns out that there are still n `independent' values, so the transformation can still be carried out in-place. For RealDoubleFFT_Radix2, the correspondence is as follows:

Logical		Physical
Re(D[0])	=	data[0]
Im(D[0])	=	0
Re(D[1])	=	data[1]
Im(D[1])	=	data[n-1]
...		...
Re(D[k])	=	data[k]
Im(D[k])	=	data[n-k]
...		...
Re(D[n/2])	=	data[n/2]
Im(D[n/2])	=	0
...		...
Re(D[n-k])	=	data[k]
Im(D[n-k])	=	-data[n-k]
...		...
Re(D[n-1])	=	data[1]
Im(D[n-1])	=	-data[n-1]

Author:

Bruce R. Miller bruce.miller@nist.gov, Contribution of the National Institute of Standards and Technology,, not subject to copyright., Derived from GSL (Gnu Scientific Library), GSL's FFT Code by Brian Gough bjg@vvv.lanl.gov, Since GSL is released under, GPL,, this package must also be.

Constructor Summary

RealDoubleFFT_Radix2(int n)
Create an FFT for transforming n points of real, double precision data.

Method Summary

void	backtransform(double[] data, int i0, int stride) Compute the (unnomalized) inverse FFT of data, leaving it in place.
double[]	toWraparoundOrder(double[] data) Return data in wraparound order.
double[]	toWraparoundOrder(double[] data, int i0, int stride) Return data in wraparound order.
void	transform(double[] data, int i0, int stride) Compute the Fast Fourier Transform of data leaving the result in data.

Methods inherited from class math.fourierTransforms.interleaved.RealDoubleFFT

backtransform, inverse, inverse, normalization, transform

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

RealDoubleFFT_Radix2

public RealDoubleFFT_Radix2(int n)

Create an FFT for transforming n points of real, double precision data. n must be an integral power of 2.

Method Detail

transform

public void transform(double[] data,
                      int i0,
                      int stride)

Compute the Fast Fourier Transform of data leaving the result in data. See Radix2 Transform Layout for description of the resulting data layout.

Specified by:

transform in class RealDoubleFFT

backtransform

public void backtransform(double[] data,
                          int i0,
                          int stride)

Compute the (unnomalized) inverse FFT of data, leaving it in place. The data must be in the same arrangement as that produced by transform.

Specified by:

backtransform in class RealDoubleFFT

toWraparoundOrder

public double[] toWraparoundOrder(double[] data)

Return data in wraparound order.

Specified by:

toWraparoundOrder in class RealDoubleFFT

See Also:

wraparound format

toWraparoundOrder

public double[] toWraparoundOrder(double[] data,
                                  int i0,
                                  int stride)

Return data in wraparound order. i0 and stride are used to traverse data; the new array is in packed (i0=0, stride=1) format.

Specified by:

toWraparoundOrder in class RealDoubleFFT

See Also:

wraparound format