fr.cnes.sirius.patrius.math.transform

Class FastCosineTransformer

java.lang.Object

fr.cnes.sirius.patrius.math.transform.FastCosineTransformer

All Implemented Interfaces:

RealTransformer, Serializable

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, …, x_N-1 is the data set to be cosine transformed, the extended data set x₀^#, …, x_2N-3^# is defined as follows

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

Then, the standard DCT-I y₀, …, y_N-1 of the real data set x₀, …, x_N-1 is equal to half of the N first elements of the DFT of the extended data set x₀^#, …, x_2N-3^#
y_n = (1 / 2) ∑_k=0^2N-3 x_k^# 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.

Since:

1.2

Version:

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

See Also:

Serialized Form

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method and Description
protected double[]	fct(double[] f) Perform the FCT 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

FastCosineTransformer

public FastCosineTransformer(DctNormalization 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.

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)

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:

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 plus one

fct

protected double[] fct(double[] f)

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