org.apache.commons.math3.transform

## 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:
    `DftNormalization`, Serialized Form

- - ### Constructor Summary

    Constructors
    Constructor and Description
    `FastFourierTransformer(DftNormalization normalization)` Creates a new instance of this class, with various normalization conventions.

  - ### Method Summary

    Methods
    Modifier and Type | Method and Description
    --- | ---
    `Object` | `mdfft(Object mdca, TransformType type)` Deprecated. see MATH-736
    `Complex[]` | `transform(Complex[] f, TransformType type)` Returns the (forward, inverse) transform of the specified complex data set.
    `Complex[]` | `transform(double[] f, TransformType type)` Returns the (forward, inverse) transform of the specified real data set.
    `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.
    `static void` | `transformInPlace(double[][] dataRI, DftNormalization normalization, TransformType type)` Computes the standard transform of the specified complex data.

    - ### Methods inherited from class java.lang.Object

      `clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

- - ### Constructor Detail

    - #### 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 Detail

    - #### 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

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