Class FastCosineTransformer

  • All Implemented Interfaces:
    Serializable, RealTransformer

    public class FastCosineTransformer
    extends Object
    implements RealTransformer, Serializable
    Implements the Fast Cosine Transform for transformation of one-dimensional real data sets. For reference, see James S. Walker, Fast Fourier Transforms, chapter 3 (ISBN 0849371635).

    There are several variants of the discrete cosine transform. The present implementation corresponds to DCT-I, with various normalization conventions, which are specified by the parameter DctNormalization.

    DCT-I is equivalent to DFT of an even extension of the data series. More precisely, if x0, …, xN-1 is the data set to be cosine transformed, the extended data set x0#, …, x2N-3# is defined as follows

    • xk# = xk if 0 ≤ k < N,
    • xk# = x2N-2-k if N ≤ k < 2N - 2.

    Then, the standard DCT-I y0, …, yN-1 of the real data set x0, …, xN-1 is equal to half of the N first elements of the DFT of the extended data set x0#, …, x2N-3#
    yn = (1 / 2) ∑k=02N-3 xk# exp[-2πi nk / (2N - 2)]     k = 0, …, N-1.

    The present implementation of the discrete cosine transform as a fast cosine transform requires the length of the data set to be a power of two plus one (N = 2n + 1). Besides, it implicitly assumes that the sampled function is even.

    See Also:
    Serialized Form
    • Constructor Detail

      • FastCosineTransformer

        public FastCosineTransformer​(DctNormalization 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

      • transform

        public double[] transform​(double[] f,
                                  TransformType type)
                           throws MathIllegalArgumentException
        Returns the (forward, inverse) transform of the specified real data set.
        Specified by:
        transform in interface RealTransformer
        Parameters:
        f - the real data array to be transformed (signal)
        type - the type of transform (forward, inverse) to be performed
        Returns:
        the real transformed array (spectrum)
        Throws:
        MathIllegalArgumentException - if the length of the data array is not a power of two plus one
      • transform

        public double[] transform​(UnivariateFunction f,
                                  double min,
                                  double max,
                                  int n,
                                  TransformType type)
                           throws MathIllegalArgumentException
        Returns the (forward, inverse) transform of the specified real function, sampled on the specified interval.
        Specified by:
        transform in interface RealTransformer
        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 real transformed array
        Throws:
        MathIllegalArgumentException - if the lower bound is greater than, or equal to the upper bound
        MathIllegalArgumentException - if the number of sample points is negative
        MathIllegalArgumentException - if the number of sample points is not a power of two plus one
      • fct

        protected double[] fct​(double[] f)
                        throws MathIllegalArgumentException
        Perform the FCT algorithm (including inverse).
        Parameters:
        f - the real data array to be transformed
        Returns:
        the real transformed array
        Throws:
        MathIllegalArgumentException - if the length of the data array is not a power of two plus one