Class FastFourierTransformer

java.lang.Object
org.apache.commons.math3.transform.FastFourierTransformer
All Implemented Interfaces:
Serializable

public class FastFourierTransformer extends Object implements Serializable
Implements the Fast Fourier Transform for transformation of one-dimensional real or complex data sets. For reference, see Applied Numerical Linear Algebra, ISBN 0898713897, chapter 6.

There are several variants of the discrete Fourier transform, with various normalization conventions, which are specified by the parameter DftNormalization.

The current implementation of the discrete Fourier transform as a fast Fourier transform requires the length of the data set to be a 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
See Also:
  • Field Details

    • serialVersionUID

      static final long serialVersionUID
      Serializable version identifier.
      See Also:
    • W_SUB_N_R

      private static final double[] W_SUB_N_R
      W_SUB_N_R[i] is the real part of exp(- 2 * i * pi / n): W_SUB_N_R[i] = cos(2 * pi/ n), where n = 2^i.
    • W_SUB_N_I

      private static final double[] W_SUB_N_I
      W_SUB_N_I[i] is the imaginary part of exp(- 2 * i * pi / n): W_SUB_N_I[i] = -sin(2 * pi/ n), where n = 2^i.
    • normalization

      private final DftNormalization normalization
      The type of DFT to be performed.
  • Constructor Details

    • FastFourierTransformer

      public FastFourierTransformer(DftNormalization normalization)
      Creates a new instance of this class, with various normalization conventions.
      Parameters:
      normalization - the type of normalization to be applied to the transformed data
  • Method Details

    • bitReversalShuffle2

      private static void bitReversalShuffle2(double[] a, double[] b)
      Performs identical index bit reversal shuffles on two arrays of identical size. Each element in the array is swapped with another element based on the bit-reversal of the index. For example, in an array with length 16, item at binary index 0011 (decimal 3) would be swapped with the item at binary index 1100 (decimal 12).
      Parameters:
      a - the first array to be shuffled
      b - the second array to be shuffled
    • normalizeTransformedData

      private static void normalizeTransformedData(double[][] dataRI, DftNormalization normalization, TransformType type)
      Applies the proper normalization to the specified transformed data.
      Parameters:
      dataRI - the unscaled transformed data
      normalization - the normalization to be applied
      type - the type of transform (forward, inverse) which resulted in the specified data
    • transformInPlace

      public static void transformInPlace(double[][] dataRI, DftNormalization normalization, TransformType type)
      Computes the standard transform of the specified complex data. The computation is done in place. The input data is laid out as follows
      • dataRI[0][i] is the real part of the i-th data point,
      • dataRI[1][i] is the imaginary part of the i-th data point.
      Parameters:
      dataRI - the two dimensional array of real and imaginary parts of the data
      normalization - the normalization to be applied to the transformed data
      type - the type of transform (forward, inverse) to be performed
      Throws:
      DimensionMismatchException - if the number of rows of the specified array is not two, or the array is not rectangular
      MathIllegalArgumentException - if the number of data points is not a power of two
    • transform

      public Complex[] transform(double[] f, TransformType type)
      Returns the (forward, inverse) transform of the specified real data set.
      Parameters:
      f - the real data array to be transformed
      type - the type of transform (forward, inverse) to be performed
      Returns:
      the complex transformed array
      Throws:
      MathIllegalArgumentException - if the length of the data array is not a power of two
    • transform

      public Complex[] transform(UnivariateFunction f, double min, double max, int n, TransformType type)
      Returns the (forward, inverse) transform of the specified real function, sampled on the specified interval.
      Parameters:
      f - the function to be sampled and transformed
      min - the (inclusive) lower bound for the interval
      max - the (exclusive) upper bound for the interval
      n - the number of sample points
      type - the type of transform (forward, inverse) to be performed
      Returns:
      the complex transformed array
      Throws:
      NumberIsTooLargeException - if the lower bound is greater than, or equal to the upper bound
      NotStrictlyPositiveException - if the number of sample points n is negative
      MathIllegalArgumentException - if the number of sample points n is not a power of two
    • transform

      public Complex[] transform(Complex[] f, TransformType type)
      Returns the (forward, inverse) transform of the specified complex data set.
      Parameters:
      f - the complex data array to be transformed
      type - the type of transform (forward, inverse) to be performed
      Returns:
      the complex transformed array
      Throws:
      MathIllegalArgumentException - if the length of the data array is not a power of two
    • mdfft

      @Deprecated public Object mdfft(Object mdca, TransformType type)
      Deprecated.
      see MATH-736
      Performs a multi-dimensional Fourier transform on a given array. Use transform(Complex[], TransformType) in a row-column implementation in any number of dimensions with O(N×log(N)) complexity with N = n1 × n2 ×n3 × ... × nd, where nk is the number of elements in dimension k, and d is the total number of dimensions.
      Parameters:
      mdca - Multi-Dimensional Complex Array, i.e. Complex[][][][]
      type - the type of transform (forward, inverse) to be performed
      Returns:
      transform of mdca as a Multi-Dimensional Complex Array, i.e. Complex[][][][]
      Throws:
      IllegalArgumentException - if any dimension is not a power of two
    • mdfft

      @Deprecated private void mdfft(FastFourierTransformer.MultiDimensionalComplexMatrix mdcm, TransformType type, int d, int[] subVector)
      Deprecated.
      see MATH-736
      Performs one dimension of a multi-dimensional Fourier transform.
      Parameters:
      mdcm - input matrix
      type - the type of transform (forward, inverse) to be performed
      d - index of the dimension to process
      subVector - recursion subvector
      Throws:
      IllegalArgumentException - if any dimension is not a power of two