org.apache.commons.math3.transform

## Class FastSineTransformer

- java.lang.Object
- - org.apache.commons.math3.transform.FastSineTransformer

- All Implemented Interfaces:
    Serializable, RealTransformer

      public class FastSineTransformer
      extends Object
      implements RealTransformer, Serializable

  Implements the Fast Sine 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 sine transform. The present implementation corresponds to DST-I, with various normalization conventions, which are specified by the parameter `DstNormalization`. It should be noted that regardless to the convention, the first element of the dataset to be transformed must be zero.

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

  - x0# = x0 = 0,
  - xk# = xk if 1 ≤ k < N,
  - xN# = 0,
  - xk# = -x2N-k if N + 1 ≤ k < 2N.

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

  The present implementation of the discrete sine transform as a fast sine transform requires the length of the data to be a power of two. Besides, it implicitly assumes that the sampled function is odd. In particular, the first element of the data set must be 0, which is enforced in `transform(UnivariateFunction, double, double, int, TransformType)`, after sampling.

  Since:
    1.2
  See Also:
    Serialized Form

- - ### Constructor Summary

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

  - ### Method Summary

    Methods
    Modifier and Type | Method and Description
    --- | ---
    `protected double[]` | `fst(double[] f)` Perform the FST algorithm (including inverse).
    `double[]` | `transform(double[] f, TransformType type)` Returns the (forward, inverse) transform of the specified real data set.
    `double[]` | `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.

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

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

- - ### Constructor Detail

    - #### FastSineTransformer

          public FastSineTransformer(DstNormalization 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)

      Returns the (forward, inverse) transform of the specified real data set. The first element of the specified data set is required to be `0`.
      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, or the first element of the data array is not zero

    - #### transform

          public double[] 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. This implementation enforces `f(x) = 0.0` at `x = 0.0`.
      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:
        `NonMonotonicSequenceException` - if the lower bound is greater than, or equal to the upper bound
        `NotStrictlyPositiveException` - if the number of sample points is negative
        `MathIllegalArgumentException` - if the number of sample points is not a power of two

    - #### fst

          protected double[] fst(double[] f)
                          throws MathIllegalArgumentException

      Perform the FST algorithm (including inverse). The first element of the data set is required to be `0`.
      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, or the first element of the data array is not zero

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