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org.apache.commons.math.transform
Class FastFourierTransformer

java.lang.Object
  extended by org.apache.commons.math.transform.FastFourierTransformer
All Implemented Interfaces:
Serializable
public class FastFourierTransformer
extends Object
implements Serializable

Implements the Fast Fourier Transform for transformation of one-dimensional data sets. For reference, see Applied Numerical Linear Algebra, ISBN 0898713897, chapter 6.

There are several conventions for the definition of FFT and inverse FFT, mainly on different coefficient and exponent. Here the equations are listed in the comments of the corresponding methods.

We require the length of data set to be power of 2, this greatly simplifies and speeds up the code. Users can pad the data with zeros to meet this requirement. There are other flavors of FFT, for reference, see S. Winograd, On computing the discrete Fourier transform, Mathematics of Computation, 32 (1978), 175 - 199.

Since:
1.2
Version:
$Revision: 1070725 $ $Date: 2011-02-15 02:31:12 +0100 (mar. 15 févr. 2011) $
See Also:
Serialized Form

Constructor Summary
FastFourierTransformer()
          Construct a default transformer.
 
Method Summary
protected  Complex[] fft(Complex[] data)
          Perform the base-4 Cooley-Tukey FFT algorithm (including inverse).
protected  Complex[] fft(double[] f, boolean isInverse)
          Perform the base-4 Cooley-Tukey FFT algorithm (including inverse).
 Complex[] inversetransform(Complex[] f)
          Inversely transform the given complex data set.
 Complex[] inversetransform(double[] f)
          Inversely transform the given real data set.
 Complex[] inversetransform(UnivariateRealFunction f, double min, double max, int n)
          Inversely transform the given real function, sampled on the given interval.
 Complex[] inversetransform2(Complex[] f)
          Inversely transform the given complex data set.
 Complex[] inversetransform2(double[] f)
          Inversely transform the given real data set.
 Complex[] inversetransform2(UnivariateRealFunction f, double min, double max, int n)
          Inversely transform the given real function, sampled on the given interval.
static boolean isPowerOf2(long n)
          Returns true if the argument is power of 2.
 Object mdfft(Object mdca, boolean forward)
          Performs a multi-dimensional Fourier transform on a given array.
static double[] sample(UnivariateRealFunction f, double min, double max, int n)
          Sample the given univariate real function on the given interval.
static Complex[] scaleArray(Complex[] f, double d)
          Multiply every component in the given complex array by the given real number.
static double[] scaleArray(double[] f, double d)
          Multiply every component in the given real array by the given real number.
 Complex[] transform(Complex[] f)
          Transform the given complex data set.
 Complex[] transform(double[] f)
          Transform the given real data set.
 Complex[] transform(UnivariateRealFunction f, double min, double max, int n)
          Transform the given real function, sampled on the given interval.
 Complex[] transform2(Complex[] f)
          Transform the given complex data set.
 Complex[] transform2(double[] f)
          Transform the given real data set.
 Complex[] transform2(UnivariateRealFunction f, double min, double max, int n)
          Transform the given real function, sampled on the given interval.
static void verifyDataSet(double[] d)
          Verifies that the data set has length of power of 2.
static void verifyDataSet(Object[] o)
          Verifies that the data set has length of power of 2.
static void verifyInterval(double lower, double upper)
          Verifies that the endpoints specify an interval.
 
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Constructor Detail

FastFourierTransformer

public FastFourierTransformer()
Construct a default transformer.

Method Detail

transform

public Complex[] transform(double[] f)
                    throws IllegalArgumentException
Transform the given real data set.

The formula is $ y_n = \Sigma_{k=0}^{N-1} e^{-2 \pi i nk/N} x_k $

Parameters:
f - the real data array to be transformed
Returns:
the complex transformed array
Throws:
IllegalArgumentException - if any parameters are invalid

transform

public Complex[] transform(UnivariateRealFunction f,
                           double min,
                           double max,
                           int n)
                    throws FunctionEvaluationException,
                           IllegalArgumentException
Transform the given real function, sampled on the given interval.

The formula is $ y_n = \Sigma_{k=0}^{N-1} e^{-2 \pi i nk/N} x_k $

Parameters:
f - the function to be sampled and transformed
min - the lower bound for the interval
max - the upper bound for the interval
n - the number of sample points
Returns:
the complex transformed array
Throws:
FunctionEvaluationException - if function cannot be evaluated at some point
IllegalArgumentException - if any parameters are invalid

transform

public Complex[] transform(Complex[] f)
                    throws IllegalArgumentException
Transform the given complex data set.

The formula is $ y_n = \Sigma_{k=0}^{N-1} e^{-2 \pi i nk/N} x_k $

Parameters:
f - the complex data array to be transformed
Returns:
the complex transformed array
Throws:
IllegalArgumentException - if any parameters are invalid

transform2

public Complex[] transform2(double[] f)
                     throws IllegalArgumentException
Transform the given real data set.

The formula is $y_n = (1/\sqrt{N}) \Sigma_{k=0}^{N-1} e^{-2 \pi i nk/N} x_k$

Parameters:
f - the real data array to be transformed
Returns:
the complex transformed array
Throws:
IllegalArgumentException - if any parameters are invalid

transform2

public Complex[] transform2(UnivariateRealFunction f,
                            double min,
                            double max,
                            int n)
                     throws FunctionEvaluationException,
                            IllegalArgumentException
Transform the given real function, sampled on the given interval.

The formula is $y_n = (1/\sqrt{N}) \Sigma_{k=0}^{N-1} e^{-2 \pi i nk/N} x_k$

Parameters:
f - the function to be sampled and transformed
min - the lower bound for the interval
max - the upper bound for the interval
n - the number of sample points
Returns:
the complex transformed array
Throws:
FunctionEvaluationException - if function cannot be evaluated at some point
IllegalArgumentException - if any parameters are invalid

transform2

public Complex[] transform2(Complex[] f)
                     throws IllegalArgumentException
Transform the given complex data set.

The formula is $y_n = (1/\sqrt{N}) \Sigma_{k=0}^{N-1} e^{-2 \pi i nk/N} x_k$

Parameters:
f - the complex data array to be transformed
Returns:
the complex transformed array
Throws:
IllegalArgumentException - if any parameters are invalid

inversetransform

public Complex[] inversetransform(double[] f)
                           throws IllegalArgumentException
Inversely transform the given real data set.

The formula is $ x_k = (1/N) \Sigma_{n=0}^{N-1} e^{2 \pi i nk/N} y_n $

Parameters:
f - the real data array to be inversely transformed
Returns:
the complex inversely transformed array
Throws:
IllegalArgumentException - if any parameters are invalid

inversetransform

public Complex[] inversetransform(UnivariateRealFunction f,
                                  double min,
                                  double max,
                                  int n)
                           throws FunctionEvaluationException,
                                  IllegalArgumentException
Inversely transform the given real function, sampled on the given interval.

The formula is $ x_k = (1/N) \Sigma_{n=0}^{N-1} e^{2 \pi i nk/N} y_n $

Parameters:
f - the function to be sampled and inversely transformed
min - the lower bound for the interval
max - the upper bound for the interval
n - the number of sample points
Returns:
the complex inversely transformed array
Throws:
FunctionEvaluationException - if function cannot be evaluated at some point
IllegalArgumentException - if any parameters are invalid

inversetransform

public Complex[] inversetransform(Complex[] f)
                           throws IllegalArgumentException
Inversely transform the given complex data set.

The formula is $ x_k = (1/N) \Sigma_{n=0}^{N-1} e^{2 \pi i nk/N} y_n $

Parameters:
f - the complex data array to be inversely transformed
Returns:
the complex inversely transformed array
Throws:
IllegalArgumentException - if any parameters are invalid

inversetransform2

public Complex[] inversetransform2(double[] f)
                            throws IllegalArgumentException
Inversely transform the given real data set.

The formula is $x_k = (1/\sqrt{N}) \Sigma_{n=0}^{N-1} e^{2 \pi i nk/N} y_n$

Parameters:
f - the real data array to be inversely transformed
Returns:
the complex inversely transformed array
Throws:
IllegalArgumentException - if any parameters are invalid

inversetransform2

public Complex[] inversetransform2(UnivariateRealFunction f,
                                   double min,
                                   double max,
                                   int n)
                            throws FunctionEvaluationException,
                                   IllegalArgumentException
Inversely transform the given real function, sampled on the given interval.

The formula is $x_k = (1/\sqrt{N}) \Sigma_{n=0}^{N-1} e^{2 \pi i nk/N} y_n$

Parameters:
f - the function to be sampled and inversely transformed
min - the lower bound for the interval
max - the upper bound for the interval
n - the number of sample points
Returns:
the complex inversely transformed array
Throws:
FunctionEvaluationException - if function cannot be evaluated at some point
IllegalArgumentException - if any parameters are invalid

inversetransform2

public Complex[] inversetransform2(Complex[] f)
                            throws IllegalArgumentException
Inversely transform the given complex data set.

The formula is $x_k = (1/\sqrt{N}) \Sigma_{n=0}^{N-1} e^{2 \pi i nk/N} y_n$

Parameters:
f - the complex data array to be inversely transformed
Returns:
the complex inversely transformed array
Throws:
IllegalArgumentException - if any parameters are invalid

fft

protected Complex[] fft(double[] f,
                        boolean isInverse)
                 throws IllegalArgumentException
Perform the base-4 Cooley-Tukey FFT algorithm (including inverse).

Parameters:
f - the real data array to be transformed
isInverse - the indicator of forward or inverse transform
Returns:
the complex transformed array
Throws:
IllegalArgumentException - if any parameters are invalid

fft

protected Complex[] fft(Complex[] data)
                 throws IllegalArgumentException
Perform the base-4 Cooley-Tukey FFT algorithm (including inverse).

Parameters:
data - the complex data array to be transformed
Returns:
the complex transformed array
Throws:
IllegalArgumentException - if any parameters are invalid

sample

public static double[] sample(UnivariateRealFunction f,
                              double min,
                              double max,
                              int n)
                       throws FunctionEvaluationException,
                              IllegalArgumentException
Sample the given univariate real function on the given interval.

The interval is divided equally into N sections and sample points are taken from min to max-(max-min)/N. Usually f(x) is periodic such that f(min) = f(max) (note max is not sampled), but we don't require that.

Parameters:
f - the function to be sampled
min - the lower bound for the interval
max - the upper bound for the interval
n - the number of sample points
Returns:
the samples array
Throws:
FunctionEvaluationException - if function cannot be evaluated at some point
IllegalArgumentException - if any parameters are invalid

scaleArray

public static double[] scaleArray(double[] f,
                                  double d)
Multiply every component in the given real array by the given real number. The change is made in place.

Parameters:
f - the real array to be scaled
d - the real scaling coefficient
Returns:
a reference to the scaled array

scaleArray

public static Complex[] scaleArray(Complex[] f,
                                   double d)
Multiply every component in the given complex array by the given real number. The change is made in place.

Parameters:
f - the complex array to be scaled
d - the real scaling coefficient
Returns:
a reference to the scaled array

isPowerOf2

public static boolean isPowerOf2(long n)
Returns true if the argument is power of 2.

Parameters:
n - the number to test
Returns:
true if the argument is power of 2

verifyDataSet

public static void verifyDataSet(double[] d)
                          throws IllegalArgumentException
Verifies that the data set has length of power of 2.

Parameters:
d - the data array
Throws:
IllegalArgumentException - if array length is not power of 2

verifyDataSet

public static void verifyDataSet(Object[] o)
                          throws IllegalArgumentException
Verifies that the data set has length of power of 2.

Parameters:
o - the data array
Throws:
IllegalArgumentException - if array length is not power of 2

verifyInterval

public static void verifyInterval(double lower,
                                  double upper)
                           throws IllegalArgumentException
Verifies that the endpoints specify an interval.

Parameters:
lower - lower endpoint
upper - upper endpoint
Throws:
IllegalArgumentException - if not interval

mdfft

public Object mdfft(Object mdca,
                    boolean forward)
             throws IllegalArgumentException
Performs a multi-dimensional Fourier transform on a given array. Use inversetransform2(Complex[]) and transform2(Complex[]) in a row-column implementation in any number of dimensions with O(N×log(N)) complexity with N=n1×n2×n3×...×nd, nx=number of elements in dimension x, and d=total number of dimensions.

Parameters:
mdca - Multi-Dimensional Complex Array id est Complex[][][][]
forward - inverseTransform2 is preformed if this is false
Returns:
transform of mdca as a Multi-Dimensional Complex Array id est Complex[][][][]
Throws:
IllegalArgumentException - if any dimension is not a power of two
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