Class FastCosineTransformer

  • All Implemented Interfaces:
    RealTransformer

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

    FCT is its own inverse, up to a multiplier depending on conventions. The equations are listed in the comments of the corresponding methods.

    Different from FFT and FST, FCT requires the length of data set to be power of 2 plus one. Users should especially pay attention to the function transformation on how this affects the sampling.

    As of version 2.0 this no longer implements Serializable

    Since:
    1.2
    • Constructor Detail

      • FastCosineTransformer

        public FastCosineTransformer()
        Construct a default transformer.
    • Method Detail

      • transform

        public double[] transform​(double[] f)
                           throws IllegalArgumentException
        Transform the given real data set.

        The formula is Fn = (1/2) [f0 + (-1)n fN] + ∑k=1N-1 fk cos(π nk/N)

        Specified by:
        transform in interface RealTransformer
        Parameters:
        f - the real data array to be transformed
        Returns:
        the real transformed array
        Throws:
        IllegalArgumentException - if any parameters are invalid
      • transform2

        public double[] transform2​(double[] f)
                            throws IllegalArgumentException
        Transform the given real data set.

        The formula is Fn = √(1/2N) [f0 + (-1)n fN] + √(2/N) ∑k=1N-1 fk cos(π nk/N)

        Parameters:
        f - the real data array to be transformed
        Returns:
        the real transformed array
        Throws:
        IllegalArgumentException - if any parameters are invalid
      • transform2

        public double[] 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 Fn = √(1/2N) [f0 + (-1)n fN] + √(2/N) ∑k=1N-1 fk cos(π nk/N)

        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 real transformed array
        Throws:
        FunctionEvaluationException - if function cannot be evaluated at some point
        IllegalArgumentException - if any parameters are invalid
      • inversetransform

        public double[] inversetransform​(double[] f)
                                  throws IllegalArgumentException
        Inversely transform the given real data set.

        The formula is fk = (1/N) [F0 + (-1)k FN] + (2/N) ∑n=1N-1 Fn cos(π nk/N)

        Specified by:
        inversetransform in interface RealTransformer
        Parameters:
        f - the real data array to be inversely transformed
        Returns:
        the real inversely transformed array
        Throws:
        IllegalArgumentException - if any parameters are invalid
      • inversetransform2

        public double[] inversetransform2​(double[] f)
                                   throws IllegalArgumentException
        Inversely transform the given real data set.

        The formula is fk = √(1/2N) [F0 + (-1)k FN] + √(2/N) ∑n=1N-1 Fn cos(π nk/N)

        Parameters:
        f - the real data array to be inversely transformed
        Returns:
        the real inversely transformed array
        Throws:
        IllegalArgumentException - if any parameters are invalid
      • inversetransform2

        public double[] 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 fk = √(1/2N) [F0 + (-1)k FN] + √(2/N) ∑n=1N-1 Fn cos(π nk/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 real inversely transformed array
        Throws:
        FunctionEvaluationException - if function cannot be evaluated at some point
        IllegalArgumentException - if any parameters are invalid