Class FastCosineTransformer

java.lang.Object
org.hipparchus.transform.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:
  • Constructor Details

    • 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 Details

    • 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