Class FastFourierTransformer

java.lang.Object
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:
  • Constructor Details

    • FastFourierTransformer

      public FastFourierTransformer()
      Construct a default transformer.
  • Method Details

    • 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