Class 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.

    See Also:
    DftNormalization, Serialized Form
    • 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:
        MathIllegalArgumentException - 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:
        MathIllegalArgumentException - if the lower bound is greater than, or equal to the upper bound
        MathIllegalArgumentException - 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