fr.cnes.sirius.patrius.math.transform

Class FastSineTransformer

java.lang.Object

fr.cnes.sirius.patrius.math.transform.FastSineTransformer

All Implemented Interfaces:

RealTransformer, Serializable

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, …, x_N-1 is the data set to be sine transformed, the extended data set x₀^#, …, x_2N-1^# is defined as follows

• x₀^# = x₀ = 0,
• x_k^# = x_k if 1 ≤ k < N,
• x_N^# = 0,
• x_k^# = -x_2N-k if N + 1 ≤ k < 2N.

Then, the standard DST-I y₀, …, y_N-1 of the real data set x₀, …, x_N-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^#, …, x_2N-1^#
y_n = (i / 2) ∑_k=0^2N-1 x_k^# 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

Version:

$Id: FastSineTransformer.java 18108 2017-10-04 06:45:27Z bignon $

See Also:

Serialized Form

Constructor Summary

Constructors

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

Method Summary

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 normalizationIn)

Creates a new instance of this class, with various normalization conventions.

Parameters:

normalizationIn - 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)

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