RealDoubleFFT.java

package com.isti.traceview.jnt.FFT;

/**
 * Abstract Class representing FFT's of real, double precision data. Concrete
 * classes are typically named RealDoubleFFT_<i>method</i>, implement the FFT
 * using some particular method.
 * <P>
 * The physical layout of the mathematical data d[i] in the array data is as
 * follows:
 * 
 * <PRE>
 * d[i] = data[i0 + stride * i]
 * </PRE>
 * 
 * The FFT (D[i]) of real data (d[i]) is complex, but restricted by symmetry:
 * 
 * <PRE>
 * D[n - i] = conj(D[i])
 * </PRE>
 * 
 * It turns out that there are still n `independent' values, so the
 * transformation can still be carried out in-place. However, each Real FFT
 * method tends to leave the real and imaginary parts distributed in the data
 * array in its own unique arrangment.
 * <P>
 * You must consult the documentation for the specific classes implementing
 * RealDoubleFFT for the details. Note, however, that each class's backtransform
 * and inverse methods understand thier own unique ordering of the transformed
 * result and can invert it correctly.
 * 
 * @author Bruce R. Miller bruce.miller@nist.gov
 * @author Contribution of the National Institute of Standards and Technology,
 * @author not subject to copyright.
 */

public abstract class RealDoubleFFT {
	int n;

	/** Create an FFT for transforming n points of real, double precision data. */
	public RealDoubleFFT(int n) {
		if (n <= 0)
			throw new IllegalArgumentException(
					"The transform length must be >=0 : " + n);
		this.n = n;
	}

	protected void checkData(double data[], int i0, int stride) {
		if (i0 < 0)
			throw new IllegalArgumentException("The offset must be >=0 : " + i0);
		if (stride < 1)
			throw new IllegalArgumentException("The stride must be >=1 : "
					+ stride);
		if (i0 + stride * (n - 1) + 1 > data.length)
			throw new IllegalArgumentException(
					"The data array is too small for " + n + ":" + "i0=" + i0
							+ " stride=" + stride + " data.length="
							+ data.length);
	}

	/** Compute the Fast Fourier Transform of data leaving the result in data. */
	public void transform(double data[]) {
		transform(data, 0, 1);
	}

	/** Compute the Fast Fourier Transform of data leaving the result in data. */
	public abstract void transform(double data[], int i0, int stride);

	/**
	 * Return data in wraparound order.
	 * 
	 * @see <a href="package-summary.html#wraparound">wraparound format</A>
	 */
	public abstract double[] toWraparoundOrder(double data[]);

	/**
	 * Return data in wraparound order. i0 and stride are used to traverse data;
	 * the new array is in packed (i0=0, stride=1) format.
	 * 
	 * @see <a href="package-summary.html#wraparound">wraparound format</A>
	 */
	public abstract double[] toWraparoundOrder(double data[], int i0, int stride);

	/** Compute the (unnomalized) inverse FFT of data, leaving it in place. */
	public void backtransform(double data[]) {
		backtransform(data, 0, 1);
	}

	/** Compute the (unnomalized) inverse FFT of data, leaving it in place. */
	public abstract void backtransform(double data[], int i0, int stride);

	/**
	 * Return the normalization factor. Multiply the elements of the
	 * backtransform'ed data to get the normalized inverse.
	 */
	public double normalization() {
		return 1.0 / ((double) n);
	}

	/** Compute the (nomalized) inverse FFT of data, leaving it in place. */
	public void inverse(double data[]) {
		inverse(data, 0, 1);
	}

	/** Compute the (nomalized) inverse FFT of data, leaving it in place. */
	public void inverse(double data[], int i0, int stride) {
		backtransform(data, i0, stride);

		/* normalize inverse fft with 1/n */
		double norm = normalization();
		for (int i = 0; i < n; i++)
			data[i0 + stride * i] *= norm;
	}

}